Exercises and Problems in Calculus by John M. Erdman
About this book :-
"Exercises and Problems in Calculus" by John M. Erdman is a practice-focused "calculus" book designed to strengthen students’ understanding through active problem solving. Rather than emphasizing long theory explanations, the book helps learners apply key ideas by working through carefully structured exercises. It is suitable for students studying introductory calculus, analytic geometry, or preparing for higher-level mathematics.
The book covers essential topics such as "functions", "limits", "continuity", and "differentiation", with problems arranged by subject area for easy reference. Each section begins with brief background notes that clarify definitions and notation before moving into exercises. Many problems use a fill-in-the-blank format to support guided learning, while others require full written solutions to develop logical reasoning and mathematical clarity.
Overall, this book is an excellent resource for improving "problem-solving" skills and reinforcing "conceptual understanding". With answers provided for selected exercises, it supports independent study as well as classroom use. Erdman’s approach encourages consistent practice, making the book especially valuable for students who learn best by doing and want to build confidence in calculus through structured repetition and challenge.
Book Detail :-
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 Author :-
The author
John M. Erdman
is a "mathematician" and experienced "educator" who served as a professor at Portland State University in the United States. He spent many years teaching calculus and related mathematical subjects, focusing on helping students develop strong foundations through practice and clear reasoning. He is best known for "Exercises and Problems in Calculus", a book that reflects his emphasis on "problem-solving", structured practice, and "conceptual understanding". Erdman’s work supports effective "learning" by encouraging students to actively engage with calculus concepts rather than memorizing formulas.
Book 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
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