Exercises and Problems in Calculus by John M. Erdman
Exercises and Problems in Calculus - Table of Contents
- PART 1. PRELIMINARY MATERIAL
- 1. Inequalities and Absolute Values
- 2. Lines in the Plane
- 3. Functions
- PART 2. LIMITS AND CONTINUITY
- 4. Limits
- 5. Continuity
- PART 3. DIFFERENTIATION OF FUNCTIONS OF A SINGLE VARIABLE
- 6. Definition of the Derivative
- 7. Techniques of Differentiation
- 8. The Mean Value Theorem
- 9. L’Hôpital’s Rule
- 10. Monotonicity and Concavity
- 11. Inverse Functions
- 12. Applications of the Derivative
- PART 4. INTEGRATION OF FUNCTIONS OF A SINGLE VARIABLE
- 13. The Riemann Integral
- 14. The Fundamental Theorem of Calculus
- 15. Techniques of Integration
- 16. Applications of the Integral
- PART 5. SEQUENCES AND SERIES
- 17. Approximation by Polynomials
- 18. Sequences of Real Numbers
- 19. Infinite Series
- 20. Convergence Tests for Series
- 21. Power Series
- PART 6. SCALAR FIELDS AND VECTOR FIELDS
- 22. Vector and Metric Properties of Rn
- 23. Limits of Scalar Fields
- PART 7. DIFFERENTIATION OF FUNCTIONS OF SEVERAL VARIABLES
- 24. Partial Derivatives
- 25. Gradients of Scalar Fields and Tangent Planes
- 26. Matrices and Determinants
- 27. Linear Maps
- 28. Definition of the Derivative
- 29. Differentiation of Functions of Several Variables
- 30. More Applications of the Derivative
- PART 8. PARAMETRIZED CURVES
- 31. Parametrized Curves
- 32. Acceleration and Curvature
- PART 9. MULTIPLE INTEGRALS
- 33. Double Integrals
- 34. Surfaces
- 35. Surface Area
- 36. Triple Integrals
- 37. Change of Variables in an Integral
- 38. Vector Fields
- PART 10. THE CALCULUS OF DIFFERENTIAL FORMS
- 39. Differential Forms
- 40. The Exterior Differential Operator
- 41. The Hodge Star Operator
- 42. Closed and Exact Differential Forms
- PART 11. THE FUNDAMENTAL THEOREM OF CALCULUS
- 43. Manifolds and Orientation
- 44. Line Integrals
- 45. Surface Integrals
- 46. Stokes’ Theorem
What You Will Learn in Exercises and Problems in Calculus
Exercises and Problems in Calculus by John Erdman is a comprehensive workbook designed to strengthen students' understanding of single-variable and multivariable calculus. An excellent companion to undergraduate mathematics courses, it serves as a valuable resource for calculus practice, problem solving, and exam preparation.
The book covers limits, differentiation, integration, sequences, series, and vector calculus through carefully organized exercises and fully worked solutions. Each section helps students develop calculus reasoning, analytical skills, and mathematical problem-solving with confidence.
Trusted by students and instructors alike, this problem book is ideal for classroom study, self-learning, and revision. Erdman's practical approach equips learners with the essential skills required for mastering calculus concepts and advanced mathematical techniques.
Book Details & Specifications
Title:
Exercises and Problems in Calculus by John M. Erdman
Publisher:
Portland State University
Year:
2013
Pages:
706
Type:
PDF
Language:
English
ISBN-10 #:
0486432777
ISBN-13 #:
978-0486432779
License:
External University Resource
Amazon:
Amazon
About the Author: John M. Erdman
The author John M. Erdman
is an Emeritus Professor of Mathematics at Portland State University, recognized for his long academic career and contributions to undergraduate mathematics education, particularly in calculus instruction.
Through years of teaching and curriculum development, Professor Erdman has produced practical learning resources that combine mathematical theory with problem-solving practice, helping students build strong foundations in calculus, mathematical analysis, and undergraduate mathematics.
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