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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