CLP-1 Differential Calculus

How to use this book
I The questions
Limits
Drawing Tangents and a First Limit
Another Limit and Computing Velocity
The Limit of a Function
Calculating Limits with Limit Laws
Limits at Infinity
Continuity
Derivatives
Revisiting tangent lines
Definition of the derivative
Interpretations of the derivative
Arithmetic of derivatives - a differentiation toolbox
Proofs of the arithmetic of derivatives
Using the arithmetic of derivatives - examples
Derivatives of Exponential Functions
Derivatives of trigonometric functions
One more tool - the chain rule
The natural logarithm
Implicit Differentiation
Inverse Trigonometric Functions
The Mean Value Theorem
Higher Order Derivatives
Applications of derivatives
Velocity and acceleration
Related Rates
Exponential Growth and Decay
Carbon Dating
Newton's Law of Cooling
Population Growth
Further problems
Taylor polynomials
Zeroeth Approximation
First Approximation
Second Approximation
Still Better Approximations
Some Examples
Estimating Changes and x, y notation
Further Examples
The error in Taylor polynomial approximation
Further problems
Optimization
Local and global maxima and minima
Finding global maxima and minima
Max/min examples
Sketching Graphs
Domain, intercepts and asymptotes
First derivative - increasing or decreasing
Second derivative - concavity
Symmetries
A checklist for sketching
Sketching examples
L'Hôpital's Rule and indeterminate forms
Towards Integral Calculus
Introduction to antiderivatives
II Hints to problems
1.1 Drawing Tangents and a First Limit
1.2 Another Limit and Computing Velocity
1.3 The Limit of a Function
1.4 Calculating Limits with Limit Laws
1.5 Limits at Infinity
1.6 Continuity
2.1 Revisiting tangent lines
2.2 Definition of the derivative
2.3 Interpretations of the derivative
2.4 Arithmetic of derivatives - a differentiation toolbox
2.5 Proofs of the arithmetic of derivatives
2.6 Using the arithmetic of derivatives - examples
2.7 Derivatives of Exponential Functions
2.8 Derivatives of trigonometric functions
2.9 One more tool - the chain rule
2.10 The natural logarithm
2.11 Implicit Differentiation
2.12 Inverse Trigonometric Functions
2.13 The Mean Value Theorem
2.14 Higher Order Derivatives
3.1 Velocity and acceleration
3.2 Related Rates
3.3.1 Carbon Dating
3.3.2 Newton's Law of Cooling
3.3.3 Population Growth
3.3.4 Further problems
3.4.1 Zeroeth Approximation
3.4.2 First Approximation
3.4.3 Second Approximation
3.4.4 Still Better Approximations
3.4.5 Some Examples
3.4.6 Estimating Changes and x, y notation
3.4.7 Further Examples
3.4.8 The error in Taylor polynomial approximation
3.4.9 Further problems
3.5.1 Local and global maxima and minima
3.5.2 Finding global maxima and minima
3.5.3 Max/min examples
3.6.1 Domain, intercepts and asymptotes
3.6.2 First derivative - increasing or decreasing
3.6.3 Second derivative - concavity
3.6.4 Symmetries
3.6.5 A checklist for sketching
3.6.6 Sketching examples
3.7 L'Hôpital's Rule and indeterminate forms
4.1 Introduction to antiderivatives
III Answers to problems
1.1 Drawing Tangents and a First Limit
1.2 Another Limit and Computing Velocity
1.3 The Limit of a Function
1.4 Calculating Limits with Limit Laws
1.5 Limits at Infinity
1.6 Continuity
2.1 Revisiting tangent lines
2.2 Definition of the derivative
2.3 Interpretations of the derivative
2.4 Arithmetic of derivatives - a differentiation toolbox
2.5 Proofs of the arithmetic of derivatives
2.6 Using the arithmetic of derivatives - examples
2.7 Derivatives of Exponential Functions
2.8 Derivatives of trigonometric functions
2.9 One more tool - the chain rule
2.10 The natural logarithm
2.11 Implicit Differentiation
2.12 Inverse Trigonometric Functions
2.13 The Mean Value Theorem
2.14 Higher Order Derivatives
3.1 Velocity and acceleration
3.2 Related Rates
3.3.1 Carbon Dating
3.3.2 Newton's Law of Cooling
3.3.3 Population Growth
3.3.4 Further problems
3.4.1 Zeroeth Approximation
3.4.2 First Approximation
3.4.3 Second Approximation
3.4.4 Still Better Approximations
3.4.5 Some Examples
3.4.6 Estimating Changes and x, y notation
3.4.7 Further Examples
3.4.8 The error in Taylor polynomial approximation
3.4.9 Further problems
3.5.1 Local and global maxima and minima
3.5.2 Finding global maxima and minima
3.5.3 Max/min examples
3.6.1 Domain, intercepts and asymptotes
3.6.2 First derivative - increasing or decreasing
3.6.3 Second derivative - concavity
3.6.4 Symmetries
3.6.5 A checklist for sketching
3.6.6 Sketching examples
3.7 L'Hôpital's Rule and indeterminate forms
4.1 Introduction to antiderivatives
IV Solutions to problems
1.1 Drawing Tangents and a First Limit
1.2 Another Limit and Computing Velocity
1.3 The Limit of a Function
1.4 Calculating Limits with Limit Laws
1.5 Limits at Infinity
1.6 Continuity
2.1 Revisiting tangent lines
2.2 Definition of the derivative
2.3 Interpretations of the derivative
2.4 Arithmetic of derivatives - a differentiation toolbox
2.5 Proofs of the arithmetic of derivatives
2.6 Using the arithmetic of derivatives - examples
2.7 Derivatives of Exponential Functions
2.8 Derivatives of trigonometric functions
2.9 One more tool - the chain rule
2.10 The natural logarithm
2.11 Implicit Differentiation
2.12 Inverse Trigonometric Functions
2.13 The Mean Value Theorem
2.14 Higher Order Derivatives
3.1 Velocity and acceleration
3.2 Related Rates
3.3.1 Carbon Dating
3.3.2 Newton's Law of Cooling
3.3.3 Population Growth
3.3.4 Further problems
3.4.1 Zeroeth Approximation
3.4.2 First Approximation
3.4.3 Second Approximation
3.4.4 Still Better Approximations
3.4.5 Some Examples
3.4.6 Estimating Changes and x, y notation
3.4.7 Further Examples
3.4.8 The error in Taylor polynomial approximation
3.4.9 Further problems
3.5.1 Local and global maxima and minima
3.5.2 Finding global maxima and minima
3.5.3 Max/min examples
3.6.1 Domain, intercepts and asymptotes
3.6.2 First derivative - increasing or decreasing
3.6.3 Second derivative - concavity
3.6.4 Symmetries
3.6.5 A checklist for sketching
3.6.6 Sketching examples
3.7 L'Hôpital's Rule and indeterminate forms
4.1 Introduction to antiderivatives