求助：初等数学领域的经典教材

nttz

代数、几何方面比较有深度的教材有哪些？前面看了法的布尔勒的就不错，但是内容还是少了点，最好有初等函数和分析的

hbghlyj

Library Genesis Felix Klein Elementary Mathematics from a Higher Standpoint: Volume I: Arithmetic, Algebra, Analysis	Library Genesis Title:         高观点下的初等数学（第一卷）算术、代数、分析 Author(s):     [德]菲利克斯·克莱因; 舒湘芹(译); 陈义章 等(译) Series:        西方数学文化理念传播译丛

Library Genesis Title:         What is mathematics?: an elementary approach to ideas and methods Author(s):     Richard Courant, Herbert Robbins, Ian Stewart	Library Genesis 什么是数学：对思想和方法的基本研究 Author(s): [美]R‧柯朗; H‧罗宾; I‧斯图尔特(修订); 左平(译); 张饴慈(译) Series: 西方数学文化理念传播译丛 Publisher: 复旦大学出版社, Year: 2005

Library Genesis Disquisitiones Arithmeticae Author(s): Carl F. Gauss, W.C. Waterhouse, Arthur A. Clarke, J. Brinkhuis, C. Greiter Publisher: Springer, Year: 1986	Library Genesis 算术探索 Author(s): [德] 卡尔·弗里德里希·高斯

Library Genesis Introduction to Analysis of the Infinite Author(s): Leonard Euler Publisher: Springer, Year: 1990	Library Genesis Library Genesis Library Genesis 无穷分析引论 Author(s): [瑞士] 欧拉

Higher arithmetic: An Introduction to the Theory of Numbers
Author(s): H. Davenport
Publisher: Cambridge University Press, Year: 2008
Library Genesis

Library Genesis Inequalities Author(s): Hardy G. H., Littlewood J.E., Polya G. Year: 1934	Library Genesis Author(s): G.H.哈代; 利特尔伍德; 波利亚 Series: 图灵数学·统计学丛书 Publisher: 人民邮电出版社, Year: 2008

Lessons in Geometry Hadamard's Plane geometry. A reader's companion Author(s): Jacques Hadamard Translated by Mark Saul Publisher: American Mathematical Society, Year: 2008 ISBN: 0821843672, 9780821843673	Library Genesis 几何学教程 作者: J·阿达玛 出版社: 哈尔滨工业大学出版社 出版年: 2011-3

Library Genesis The Geometry of René Descartes: with a Facsimile of the First Edition (Dover Books on Mathematics)	Library Genesis 几何 Author(s): [法]笛卡尔 Series: 科学素养文库·科学元典丛书 Publisher: 北京大学出版社, Year: 2008

Library Genesis An Introduction to the Theory of Numbers, Sixth Edition Author(s): G. H. Hardy, Edward M. Wright; Editors: D. R. Heath-Brown, Joseph H. Silverman Publisher: Oxford University Press, Year: 2008	Library Genesis 数论导论 G.H.哈代

Library Genesis A course in arithmetic	Library Genesis Author(s): 塞尔; 冯克勤; 丁石孙 Series: 数学翻译丛书 Publisher: 高等教育出版社, Year: 2007

Library Genesis A friendly introduction to number theory Author(s): Joseph H Silverman Series: Featured Titles for Number Theory Publisher: Pearson, Year: 2013	Library Genesis Author(s): [美] Joseph H.Silverman Series: 华章数学译丛 Publisher: 机械工业出版社, Year: 2008

Library Genesis Number theory: an approach through history. From Hammurapi to Legendre Author(s): André Weil Publisher: Birkhäuser Boston, Year: 1987	Library Genesis 数论: 从汉穆拉比到勒让德的历史导引 Author(s): André Weil Series: 数学翻译丛书 Publisher: 高等教育出版社, Year: 2010

Library Genesis Author(s): 项武义; 王申怀; 潘养廉 Series: 现代数学基础 Publisher: 高等教育出版社, Year: 2014	Library Genesis 基础代数学 Author(s): 项武义

Library Genesis College algebra Author(s): Henry Burchard Fine Series: Ams Chelsea Publishing Publisher: American Mathematical Society, Year: 2005	Library Genesis Library Genesis Library Genesis Library Genesis 范氏大代数

Library Genesis Geometry II Author(s): Marcel Berger Series: Universitext Publisher: Springer, Year: 2009	Library Genesis Problems in geometry Author(s):        Marcel Berger, P. Pansu, J.-P. Berry, X. Saint-Raymond, Silvio Levy Series:        Problem books in mathematics

Library Genesis
射影几何趣谈
Author(s): 冯克勤
Series: 初等数学小丛书
Publisher: 上海教育出版社, Year: 1987

Library Genesis One Hundred Great Problems of Elementary Mathematics: Their History and Solution (Dover Books on Mathematics)	Library Genesis 100 个著名初等数学问题. ——历史和解. 100 Great Problems of Elementary Mathematics: Their History and Solution. [德]H·德里. Heinrich Dörrie

Library Genesis
美苏大学生数学竞赛题解: 初等数学部分
Author(s): 王志雄
Publisher: 福建科学技术出版社


Library Genesis
[法] 唐乃尔 Jules Tannery
出版社: 上海科学技术出版社
译者: 朱德祥
出版年: 1982-8
丛书: 初等数学教程


Library Genesis
CONVEX FIGURES AND POLYHEDRA
Author(s):        Lyusternik L.A.

hbghlyj

Algebra

1. 101 problems in Algebra
2. elementary-linear-algebra
3. Challenging Problems in Algebra 2E (Dover) – Posamentier . Salkind
4. Abstract Algebra Theory and Applications Thomas W. Judson
5. An_Introduction_to_Diophantine_Equations__A_Problem_Based_Approach

Combinatorics

1. Topics_in_Finite_and_Discrete_Mathematics
2. An_Introduction_to_Enumeration
3. A_Course_in_Combinatorics
4. A walk through combinatorics
5. 102 combinatorial problems
6. a_path_to_combinatorics_for_undergraduates

Number theory

1. Elementary Number Theory in Nine Chapters
   
2. naoki sato number theory
3. 104 Number Theory Problems – Titu Andreescu . Dorin Andrica . Zuming Feng
4. Solved and unsolved problems in Number Theory – Daniel Shanks
5. an introduction to the theory of numbers 5ed – niven i., zuckerman h.s., montgomery h.l
6. Primitive Roots,Order,Quadratic Residue
7. Some Own Problems In Number Theory

Game theory

1. The-Mathematics-of-Games-and-Gambling
2. Martin_J._Osborne-An_Introduction_to_Game_Theory-Oxford_University_Press,_USA(2003)
3. PhD-Strategic-Decision-Making-Theory-1999
4. comb

Geometry

1. Forum Geometricorum – All volumes
2. Geometric_Problems_on_Maxima_and_Minima
3. GeometryNotes
4. problems in plane and solid geometry
5. geometryrevisited_coxetergreitzer
6. Challenging Problems in Geometry (Dover) – Posamentier . Salkind
7. Complex Numbers in Geometry – Yaglom
8. 103 Trigonometry Problems – Titu Andreescu . Zuming Feng

Inequalities

1. Inequalities-Hardy-Littlewood-PolyaInequalities
2. A.Mathematical.Olympiad.Approach.Oct.2009
3. 567 Nice And Hard Inequality
4. THE_CAUCHY___SCHWARZ_MASTER_CLASS
5. Secrets-in-Inequalities-Volume-1
6. Inequalities A Mathematical Olympiad Approach
7. Inequalities theorems techniques zdravko
8. Basics_of_olympiad_inequalities(2008)
9. MildorfInequalities
10. KedlayaInequalities
11. Algebraic Inequalities – Old And New Methods – Vasile Cirtoaje.
12. Inequalities
13. pham king hung – secrets in inequalities (volume 1)

Old olympiad problem books

1. ussr olympiad problem book
2. putnam and beyond
3.  imo compendium
4. Mathematical_Olympiad_in_China-Problems_and_Solutions
5. From Erdos to Kiev – Problems of Olympiad Caliber – Ross Honsberger
6. Andreescu – Contests Around the World 1997-1998
7. Andreescu – Contests Around the World 1999-2000
8. Andreescu – Contests Around the World 2000-2001

University mathematics books

1. mathematics for computer science
2. random-variables-i
3. random-variables-ii
4. random-variables-iii
5. stochastic-processes-1
6. stochastic-processes-2
7. BasicCalculus
8. Calculus-of-Several-Variables-Serge-Lang
9. Calculus ron larson bruce edwards
10. lineer-algebra
11. linear-algebra-c-1
12. linear-algebra-c-2
13. linear-algebra-c-3
14. linear-algebra-c-4
15. applied-mathematics-by-example-theory
16. continuous-distributions
17. applied-mathematics-by-example-exercises
18. analytic-aids
19. introductory-finite-volume-methods-for-pdes
20. introductory-finite-difference-methods-for-pdes
21. introduction-to-probability
22. interest-rates-in-financial-analysis-and-valuation
23. integration-and-differential-equations
24. gentle-introduction-to-mathematics-for-computer
25. essential-engineering-mathematics
26. engineering-mathematics-youtube-workbook
27. discrete-distributions

General Olympiad Documents

1. Problem-Books-in-Mathematics-Problem-Solving-Strategies
2. Mathematical Problems And Proofs Combinatorics, Number Theory, and Geometry – Kluwer Academic
   
3. Lecture_Notes_on_Mathematical_Olympiad_Courses__For_Junior_Section_Vol_1__Mathematical_Olympiad_Series_
4. Lecture_Notes_on_Mathematical_Olympiad_Courses__For_Junior_Section__Vol__2__Mathematical_Olympiad_Series_
5. basic facts

TTAANN001

hbghlyj 发表于 2022-8-26 08:53
本帖最后由 hbghlyj 于 2022-8-26 01:57 编辑 Algebra

101 problems in Algebra

请问有巴赫瓦洛夫的《解析几何习题集》吗？

nttz

hbghlyj 发表于 2022-8-26 08:53
本帖最后由 hbghlyj 于 2022-8-26 01:57 编辑 Algebra

101 problems in Algebra

怎么没有高手翻译下上面的好书呢？还是不愿意做呢

nttz

hbghlyj 发表于 2022-8-26 08:53
本帖最后由 hbghlyj 于 2022-8-26 01:57 编辑 Algebra

101 problems in Algebra

101 problems in Algebra problem 32
a（n，2） 递推到a（1，2）时候，为啥最后a（1，2） = 2  呢

hbghlyj

nttz 发表于 2022-9-3 09:19
101 problems in Algebra problem 32
a（n，2） 递推到a（1，2）时候，为啥最后a（1，2） = 2  呢 ...

Problem 32
What is the coefficient of $x^2$ when
$$
(1+x)(1+2 x)(1+4 x) \cdots\left(1+2^n x\right)
$$
is expanded?

Solution 32
Let
$$
f_n(x)=a_{n, 0}+a_{n, 1} x+\cdots+a_{n, n} x^n=(1+x)(1+2 x) \cdots\left(1+2^n x\right) .
$$
It is easy to see that $a_{n,0}=1$ and
$$
a_{n, 1}=1+2+\cdots+2^n=2^{n+1}-1 .
$$
Since
$$
\begin{aligned}
f_n(x) & =f_{n-1}(x)\left(1+2^n x\right) \\
& =\left(1+\left(2^n-1\right) x+a_{n-1,2} x^2+\cdots\right)\left(1+2^n x\right) \\
& =1+\left(2^{n+1}-1\right) x+\left(a_{n-1,2}+2^{2 n}-2^n\right) x^2+\cdots,
\end{aligned}
$$
we have
$$
\begin{aligned}
a_{n, 2} & =a_{n-1,2}+2^{2 n}-2^n \\
& =a_{n-2,2}+2^{2 n-2}-2^{n-1}+2^{2 n}-2^n \\
& =\cdots \\
& =a_{1,2}+\left(2^4+2^6+\cdots+2^{2 n}\right)-\left(2^2+2^3+\cdots+2^n\right) \\
& =2+\frac{2^4\left(2^{2 n-2}-1\right)}{3}-4\left(2^{n-1}-1\right) \\
& =\frac{2^{2 n+2}-3 \cdot 2^{n+1}+2}{3}=\frac{\left(2^{n+1}-1\right)\left(2^{n+1}-2\right)}{3}
\end{aligned}
$$

hbghlyj

TTAANN001 发表于 2022-8-27 03:53
请问有巴赫瓦洛夫的《解析几何习题集》吗？

Google Books有啊
Аналитическая геометрия
учебник для педагогических институтов
By Сергей Владимирович Бахвалов · 1958

hbghlyj

USA MO Olympiad Problem Solving:

Problem solving and proofs at the Olympiad level are an entirely different skill from the AMC and AIME competitions.

It is assumed you've completed the Art of Problem Solving Volume 1 and at least some of Volume 2. There are a number of books both classical and modern that cover non-routine problem solving at the Olympiad level. The classical resources on problem solving are mostly by the famous mathematician George Polya.

Classical treatments on Problem Solving:

1. How to Solve It - Polya

2. Mathematical Discovery Polya

3. Mathematics and Plausible Reasoning I Polya

4. Mathematics and Plausible Reasoning II (2nd edition) Polya

Modern treatments on Problem Solving::

1. Math Olympiad Dark Arts

Olympiad Problem Collections:

General advanced problem collections are a good place to start, covering a range of topics. They will also help you with your AIME performance, necessary for Olympiad qualification. Of course, your main focus should be to practice completely the past problems of the Olympiad you are preparing for, USAJMO, USAMO, etc. It is assumed you've completed the Art of Problem Solving Volume 1 and most of Volume 2. The famous general collections from Russia, Poland, and Hungary should be well studied. I find the Polish book to still be the most relevant for really learning Olympiad level proofs..

Classical Problem Collections::

1. Problems in Elementary Mathematics - Lidsky

2. Mathematical Problems and Puzzles from the Polish Mathematical Olympiads - Straszewicz (1965)

3. USSR Olympiad Problem Book (The) - Shklasrsky, Chentzov, and Yaglom (1993, Dover) (1-1)

4. Hungarian Problem Book I (1894 - 1905) - Rapaport (MAA,1963)

5. Hungarian Problem Book II (1906 - 1928) - Rapaport (MAA,1963)

6. Hungarian Problem Book III (1929 - 1943) - Andy Liu (MAA,2001)

7. Hungarian Problem Book IV (1894 - 1905) - Barrington, Liu, (MAA,2011)

Geometry: Plane Geometry

It is assumed you've completed the Art of Problem Solving Introduction to Geometry. In my view, the classical plane geometry resources are still the superior choices for study, even though they are very dense. Start with #1, #2, and #3 (Challenging Problems and Geometry Revisited), however, to do well on the Olympiad, you will need to study the more advanced Altshiller-Court, Johnson, and Aref. Altshiller-Court and Johnson are very light on problems, Aref is heavy on problems, so they all work together. Everything you need for Olympiad plane geometry success is right here.

Classical treatments:

1. Challenging Problems in Geometry by Alfred Posamentier.pdf

3. Geometry Revisited (New Mathematical Library 19) by H. Coxeter, S. Greitzer (MAA, 1967).pdf

4. An Introduction to the Modern Geometry of the Triangle and the Circle by Nathan Altshiller-Court (Dover 2007).pdf"

5. Advanced Euclidean Geometry by Roger Johnson (Dover, 1960).pdf

6. Problems and Solutions in Euclidean Geometry by Aref, Wernick (Dover, 1968).pdf"

Modern treatments::

Problem-Solving and Selected Topics in Euclidean Geometry In the Spirit of the Mathematical Olympiads by Louridas, Rassias (2013)

Algebra: Equations and Trigonometry:

It is assumed that you've completed and understand both Art of Problem Solving Introduction to Algebra and Art of Problem Solving Intermediate Algebra.
In my view, the classical Algebra problem books are still the superior choices for study.

1. Problems in Elementary Mathematics - Lidsky

2. Problems in Higher Algebra - Faddeev

3. A Problem Book in Algebra - Krechmar

Inequalities - Geometric and Analytic

The modern resources are far superior choices for study than the older books as they are oriented towards Olympiad competition study. Start with the tutorials and then the modern books and then if your really inspired take a look at the classical and other books, everything you will need is in the tutorials and modern books. The classical resources include large amounts of material that is not relevant for high school olympiad contests and though interesting, can eat up your time.

Tutorial Introductions:

1. A less than B (Inequalities) - Kedlaya (1999).pdf (ab 37 page introduction)

2. Topics in Inequalities 1st edition - Hojoo Lee (2007).pdf (a longer 82 page introduction)

3. Olympiad Inequalities - Thomas Mildorf (2006).pdf (the basic 12 olympiad inequalities)

Modern Treatments:

4. Inequalities A Mathematical Olympiad Approach - Manfrino, Ortega, and Delgado (Birkhauser, 2009).pdf

5. Basics of Olympiad Inequalities - Riasat S.(2008).pdf

6. Inequalities - Theorems, Techniques, and Selected Problems - Cvetkovski (Springer, 2011).pdf

7. Equations and Inequalities - Elementary Problems and Theorems in Algebra and Number Theory - Jiri Herman (2000, CMS).pdf (Chapter 2)

Classical Treatments:

Elementary Inequalities - Mitrinovic, et. al. (1964, Noordhoff).pdf

Geometric Inequalities - Bottema, et. al. (1968).pdf

An Introduction To Inequalities (New Mathematical Library 3) - Beckenbach and Bellman.pdf

Geometric Inequalities (New Mathematical Library 4) - Kazarinoff.pdf

Analytic Inequalities - Kazarinoff (1961, Holt).pdf

Analytic Inequalities - Mitrinovic, Dragoslav S., (Springer, 1970).pdf

Inequalities - Beckenbach E., Bellman R. 1961.pdf

Additional Olympiad Inequalities Problem Books and References:

Algebraic Inequalities (Old and New Methods) - Cirtoaje.pdf

Old and New Inequalities - Andreescu.pdf

Secrets in Inequalities (volume 1) Pham Kim Hung.pdf

Geometric Problems on Maxima and Minima - Titu Andreescu, Oleg Mushkarov, Luchezar Stoyanov.pdf

An Introduction To The Art of Mathematical Inequalities - Steele, J. Michael (2004, MAA).pdf

When Less is More - Visualizing Basic Inequalities (Dolciani 36) - Alsina and Nelson (2009, MAA).pdf

Functional Equations:

There are no classical books and resources on olympiad functional equations problems.It was all hit or miss back then from various magazine problem sections. Start with the tutorials, then on to the modern books, then it's just a matter of doing problems. Treat each one as a puzzle.

1. The Quest for Functions (Tutorial - Beginner) by Vaderlind (2005).

2. Functional Equations (Tutorial - Advanced) by Radovanovic (2007).

3. Functional Equations by Andreescu, Boreico (2007)

4. Functional Equations and How To Solve Them by Small (Springer, 2007)

5. Functional Equations by Leigh-Lancaster (2006).

6. 100 Functional Equations from AoPS.

Discrete Mathematics (Combinatorics, Probability, and Graph Theory):

It is assumed you've finished the Art of Problem Solving Counting and Probability book. The modern treatments are far superior to the classical resources. There are a number of good textbooks for background, but most include too much as they are oriented towards college courses. The idea is to pick one and learn it well. I always liked the Tucker book, now in a 6th edition. The Tucker and Vilenkin books have great coverage of generating functions. The Art of Problem Solving Intermediate Counting is good also.

1. Applied Combinatorics by Alan Tucker

2. Counting, 2nd Edition - Meng, Guan (2013)

3. Principles and Techniques in Combinatorics - Chen Chuan-Chong, Koh Khee-Meng (WS, 1992).pdf

4. Combinatorics - Vilenkin N.(1971).pdf

Number Theory:

It is assumed that you've covered the matieral in the Art of Problem Solving Introduction to Number Theory. The necessary background for Olympiad level number theory can be found in any of dozens of books available that are usually titled "Elementary Number Theory" or some variation. The idea is to pick one and learn it well. Generally they don't cover diophantine equations that well, which is where the Olympiad problem books come in. The Sierpinski book is the best. Note that at the international olympiad level, you now must also know quadratic reciprocity. The ones I like are by Roberts, LeVeque, and Dudley. The Roberts book is very unusual for style. Once you know the basics it really is all about doing problems.

1. Elementary Number Theory - A Problem Solving Approach - Roberts (MIT, 1977).pdf

2. Elementary Number Theory - Dudley

3. 250 Problems in Elementary Number Theory - Sierpinski (1970).pdf

4. An Introduction to Diophantine Equations - A Problem-Based Approach - Andreescu, Andrica and Cucurezeanu (Birk, 2011).pdf

5. 1001 Problems in Classical Number Theory (Problems).pdf

Proof Techniques: Game Theory

1001 Problems in Classical Number Theory (Solutions).pdf

2008 MOP Blue Functional Equations-I

2008 MOP Blue Functional Equations-II

Basic 7th Lesson FunctionalEquations0108

2010 Functional Equations

2009 Functional Equations, Peng Shi

2010 Functional Equations Solutions

2007 Functional Equations, Jacob Steinhardt

2009.3 Functional Equations, Brian Hamrick

Functional Equations Solutions

2010.9 Functional Equations, Mitchell Lee

2010 Functional Equations, Mitchell Lee

2011 Functional Equations, Po-Shen Loh

hbghlyj

Igor Kortchemski's web page
Full courses in French:

• Arithmetic - PDF (by Pierre Bornsztein, Xavier Caruso, Pierre Nolin, Mehdi Tibouchi)
• Functional equations - PDF (by Pierre Bornsztein and Moubinool Omarjee)
• Geometry - PDF (by Pierre Dehornoy)
• Graphs - PDF (by Pierre Bornsztein)
• Inequalities - PDF (by Pierre Bornsztein)

Courses in English:

• Notes on Euclidean Geometry - PDF (by Kiran Kedlaya)
• A Tour de Force in Geometry - PDF (by Thomas Mildorf)
• Number Theory - PDF (by Naoki Sato)
• Olympiad Inequalities - PDF (by Thomas Mildorf)
• Topics in Inequalities - Theorems and Techniques - PDF (Hojoo Lee)
• A<B - PDF (Kiran Kedlaya)

My interventions
Here are some of the courses I have written at various internships:

• Arithmetic: LTE theorem, order, cyclotomic polynomials and theorem of 'sigomondy' (with exercises)
• Polynomials: courses (with exercises)
• Mini combinatoric crooks
• Scalar product, power from a point with respect to a circle and geometry of the triangle: lessons with some exercises

Here are compilations of exercises by theme:

• Arithmetic: Order, LTE Theorem, Diophant Equations Modulo N, Vieta Jumping, Cyclothomic Polynomials, Theorem of zigmondy
• Combination: probabilistic combinatorial

Miscellaneous and varied exercises

• All IMO topics between 1990 and 2002 - PDF
• Mathematical Olympiads 1996-1997: Olympiad Problems from Around the World - PDF
• Mathematical Olympiads 1997-1998: Olympiad Problems from Around the World - PDF
• IMO Geomety Problems (Hojoo Lee) - PDF
• Inequalities through problems (Hojoo Lee) - PDF
• Inequalities (Hojoo Lee) - Problem Set 1 (PDF) - Problem Set 2 (PDF)
• Problems in elementary number theory (Hojoo Lee) - PDF

Geometry Problems from IMOs
Problems in Elementary Number Theory

hbghlyj

书名包含An Elementary Treatise都属于初等数学领域

Apollonius of Perga, Thomas Little Heath	Treatise on Conic Sections
Issac Todhunter	An elementary treatise on the theory of equations: with a collection of examples. [3 ed.]
Benjamin Peirce	An elementary Treatise on Plane and Solid Geometry
Charles Smith	An Elementary Treatise on Solid Geometry [11th ed.]
Percival Frost	An Elementary Treatise on Curve Tracing [5th ed.]
A. B. Basset	An elementary treatise on cubic and quartic curves [CUP ed.]
Robert Lachlan	An Elementary Treatise on Modern Pure Geometry
W. J. Johnston	An Elementary Treatise on Analytical Geometry, with Numerous Examples
Grund, Francis Joseph	An elementary treatise on geometry : simplified for beginners not versed in algebra. Part I, containing plane geometry, with its application to the solution of problems [3rd ed., stereotyped.]
Joseph Edwards	An Elementary Treatise on the Differential Calculus: With Applications and Numerous Examples
Charles L. Dodgson	An elementary treatise on determinants
William Woolsey Johnson; John Minot Rice	An elementary treatise on the differential calculus founded on the method of rates or fluxions. [3d rev. ed.]
Henry Thomas Herbert Piaggio	An elementary treatise on differential equations and their applications
Arthur Cayley	An elementary treatise on elliptic functions [2nd ed.]
Thomas Murray MacRobert	An elementary treatise on harmonic functions, with applications [2nd ed.]
William Elwood Byerly	An elementary treatise on Fourier's series and spherical, cylindric, and ellipsoidal harmonics: With Applications to Problems in Mathematical Physics
Jellett J.H.	An elementary treatise on calculus of variations (1850)
Isaac Todhunter	An Elementary Treatise On Laplace's Functions, Lame's Functions and Bessel's Functions [Elibron Classics ed.]
John Minot Rice, William Woolsey Johnson	An Elementary Treatise on the Differential Calculus Founded on the Method of Rates or Fluxions
N. M. Ferrers	An elementary treatise on spherical harmonics and subjects connected with them
George Biddell Airy, K.C.B., M.A., LL.D., D.C.L.	An elementary treatise on partial differential equations. Designed for the use of students in the university (2nd edition, 1873) [2nd ed.]
Tait P.G.	An elementary treatise on quaternions [3ed.]
H. Piaggio	An Elementary Treatise on Diff. Eqns. and Their Applns.