Calculus I
Rao W. O.
,
, Contents
Course description iv
References iv
Part 1. The First Part 1
Chapter 1. Limits and Continuity 2
1.1. Limits of Functions 2
1.2. Limits at Infinity and Infinite Limits 7
1.3. Continuity 10
Chapter 2. Derivatives 15
2.1. Tangent Lines and Their Slopes 15
2.2. The Derivative 18
2.3. Differentiation Rules 22
2.4. Derivatives of trigonometric functions 26
2.5. Higher Order Derivatives 30
2.6. Implicit Differentiation 32
2.7. Parametric Differentiation 33
Chapter 3. Transcedental Functions 38
3.1. Inverse Functions 38
3.2. Exponential and Logarithmic Functions 43
3.3. Inverse Trigonometric Functions 49
3.4. Hyperbolic Functions 54
Chapter 4. Applications of Diferentiation 58
4.1. Using differentials and derivatives 58
4.2. Mean value theorems of differential calculus 63
4.3. Related Rates 64
4.4. Indeterminate Forms 66
4.5. Extreme Values 68
4.6. Curve Sketching 76
4.7. Linear Approximations 80
4.8. Taylor Polynomial 83
iii
, Course description
Limits and continuity of functions. Differentiation of functions of a single variable, para-
metric and implicit differentiation. Antiderivatives and applications to areas and volumes
of revolution. Integration by substitution. Applications of differentiation, mean value
theorems of differential calculus.
References
1. Calculus: A complete course by Robert A. Adams and Christopher Essex.
iv
Rao W. O.
,
, Contents
Course description iv
References iv
Part 1. The First Part 1
Chapter 1. Limits and Continuity 2
1.1. Limits of Functions 2
1.2. Limits at Infinity and Infinite Limits 7
1.3. Continuity 10
Chapter 2. Derivatives 15
2.1. Tangent Lines and Their Slopes 15
2.2. The Derivative 18
2.3. Differentiation Rules 22
2.4. Derivatives of trigonometric functions 26
2.5. Higher Order Derivatives 30
2.6. Implicit Differentiation 32
2.7. Parametric Differentiation 33
Chapter 3. Transcedental Functions 38
3.1. Inverse Functions 38
3.2. Exponential and Logarithmic Functions 43
3.3. Inverse Trigonometric Functions 49
3.4. Hyperbolic Functions 54
Chapter 4. Applications of Diferentiation 58
4.1. Using differentials and derivatives 58
4.2. Mean value theorems of differential calculus 63
4.3. Related Rates 64
4.4. Indeterminate Forms 66
4.5. Extreme Values 68
4.6. Curve Sketching 76
4.7. Linear Approximations 80
4.8. Taylor Polynomial 83
iii
, Course description
Limits and continuity of functions. Differentiation of functions of a single variable, para-
metric and implicit differentiation. Antiderivatives and applications to areas and volumes
of revolution. Integration by substitution. Applications of differentiation, mean value
theorems of differential calculus.
References
1. Calculus: A complete course by Robert A. Adams and Christopher Essex.
iv
