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Book Contents :-
Schaum's Outline of Theory and Problems of Beginning Calculus (2nd Edition) written by Elliott Mendelson cover the following topics.
1. Coordinate Systems on a Line
1.1 The Coordinates of a Point
1.2 Absolute Value
2. Coordinate Systems in a Plane
2.1 The Coordinates of a Point
2.2 The Distance Formula
2.3 The Midpoint Formulas
3. Graphs of Equations
4. Straight Lines
4.1 Slope
4.2 Equations of a Line
4.3 Parallel Lines
4.4 Perpendicular Lines
5. Intersections of Graphs
6. Symmetry
6.1 Symmetry about a Line
7. Functions and Their Graphs

7.1 The Notion of a Function
7.2 Intervals
7.3 Even and Odd Functions
7.4 Algebra Review: Zeros of Polynomials
8. Limits
8.1 Introduction
8.2 Properties of Limits
8.3 Existence or Nonexistence of the Limit
9. Special Limits
9.1 One-Sided Limits
9.2 Infinite Limits: Vertical Asymptotes
9.3 Limits at Infinity: Horizontal Asymptotes
10. Continuity
10.1 Definition and Properties
10.2 One-Sided Continuity
10.3 Continuity over a Closed Interval
11. The Slope of a Tangent Line
12. The Derivative
13. More on the Derivative
13.1 Differentiability and Continuity
13.2 Further Rules for Derivatives
14. Maximum and Minimum Problems
14.1 Relative Extrema
14.2 Absolute Extrema
15. The Chain Rule
15.1 Composite Functions
15.2 Differentiation of Composite Functions
16. Implicit Differentiation
17. The Mean-Value Theorem and the Sign of the Derivative
17.1 Rolle's Theorem and the Mean-Value Theorem
17.2 The Sign of the Derivative
18. Rectilinear Motion and Instantaneous Velocity
19. Instantaneous Rate of Change
20. Related Rates
21. Approximation by Differentials; Newton's Method
21.1 Estimating the Value of a Function
21.2 The Differential
21.3 Newton's Method
22. Higher-Order Derivatives
23. Applications of the Second Derivative and Graph Sketching
23.1 Concavity
23.2 Test for Relative Extrema
23.3 Graph Sketching
24. More Maximum and Minimum Problems
25. Angle Measure
25.1 Arc Length and Radian Measure
25.2 Directed Angles
26. Sine and Cosine Functions
26.1 General Definition
26.2 Properties
27. Graphs and Derivatives of Sine and Cosine Functions
27.1 Graphs
27.2 Derivatives
28. The Tangent and Other Trigonometric Functions
29. Antiderivatives
29.1 Definition and Notation
29.2 Rules for Antiderivatives
30. The Definite Integral
30.1 Sigma Notation
30.2 Area under a Curve
30.3 Properties of the Definite Integral
31. The Fundamental Theorem of Calculus
31.1 Calculation of the Definite Integral
31.2 Average Value of a Function
31.3 Change of Variable in a Definite Integral
32. Applications of Integration I: Area and Arc Length
32.1 Area between a Curve and the y-axis
32.2 Area between Two Curves
32.3 Arc Length
33. Applications of Integration II: Volume
33.1 Solids of Revolution
33.2 Volume Based on Cross Sections
34. The Natural Logarithm
34.1 Definition
34.2 Properties
35. Exponential Functions
35.1 Introduction
35.2 Properties of ax
35.3 The Function ex
36.1 L'Hôpital's Rule
36.2 Exponential Growth and Decay
36. L'Hôpital's Rule; Exponential Growth and Decay
37. Inverse Trigonometric Functions
37.1 One-One Functions 292
37.2 Inverses of Restricted Trigonometric Functions
38. Integration by Parts
39. Trigonometric Integrands and Trigonometric Substitutions
39.1 Integration of Trigonometric Functions
39.2 Trigonometric Substitutions
40. Integration of Rational Functions; The Method of Partial Fractions
Appendix
A Trigonometric Formulas
B Basic Integration Formulas
C Geometric Formulas
D Trigonometric Functions
E Natural Logarithms
F Exponential Functions
Answers to Supplementary Problem
Index
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