Calculus

Limits

Introduction to limits
Left and right limits (One Sided Limits)
Method of computing limits:

• Making a table of values
• Finding left and right limits
• Some important trigonometric limits and their proofs

What is the indeterminate form

Differential Calculus

Definition of the derivative
Derivative rules

• Power rule - Solved examples - Worksheet
• Product rule - Solved examples - Worksheet
• Quotient rule - Solved examples - Worksheet
• Trigonometric functions - Solved examples - Worksheet
• Logarithmic/exponential functions - Solved examples - Worksheet
• Chain rule - Solved examples - Worksheet

Second derivatives
Higher Order Derivatives
Methods of differentiation

• Implicit differentiation - Solved examples - Worksheet
• Logarithmic differentiation

Applications of derivatives

• Critical points
• Relative maximum and relative minimum
• Rate of change
• Tangent and normal lines

General:

• Difference between power and exponential rule

Integral Calculus

Power Rule of Integration

Integrating `1/x`

Simple substitution in integrals
Basic integration formulas
Integration problems involving simple substitutions