Introduction to Calculus

1.1: Limit and Continuity of Functions with One Variable

1.2: Properties of Limits

1.3: Properties of Limits: Practice Problems

Week 1 Quiz 1 & 2: Quiz Files

2.1: Limit of Function (x → infinity)

2.2: Properties of Infinite Limits

2.3: Infinite Limits – Practice Problems

2.4: Squeeze Theorem

2.5: Limit of Function (the number “e”)

Week 2 Quiz Files

3.1: Continuity of Functions

3.2: Three Types of Discontinuities

3.3: Algebraic Properties of Functions on the Continuity

Week 3 Quiz Files

4.1: Introduction to Derivatives

4.2: Average Rate of Change (AROC)

4.3: Instantaneous Rate of Change (IROC)

Week 4 Quiz Files

Extra Study Resource: Polynomial Expressions

5.1: Introduction to Derivative Rules

5.2: Derivatives Recap

5.3: Power Rule and Constant Rule

Week 5 Quiz Files

5.4: Power Rule and Constant Rule: Long Questions

5.5: Chain Rule

5.6: Product Rule and Quotient Rule

6.1: Derivatives of Trigonometric Functions

Week 6 Quiz Files

6.2: Derivatives of Logarithmic and Exponential Functions

6.3: Derivatives of Inverse Logarithmic and Hyperbolic Functions

6.4: Tangent and Normal of the Graph

7.1: Implicit Differentiation

Week 7 Quiz Files

7.2: Partial Differentiation

7.3: Derivatives of Higher Order

7.4: Differentiability and Continuity

7.5: Mean Value Theorem

8.1: Increasing and Decreasing Functions

Week 8 Quiz Files

8.2: Concavity and Point of Inflection

8.3: Min & Max Values, First Derivative Test, and Second Derivative Test

8.4: Extreme Value Theorem

9.1: Optimisation Part 1

9.2: Optimisation Part 2

Week 9 Quiz Files

9.3: Related Rates

9.4: Linear Approximation

10.1: Area Problem and Accumulation

10.2: Riemann Sums

10.3: Definite Integral Notation

10.4: Antiderivatives and Basic Rules

11.1: Properties of Definite Integrals

11.2: The Fundamental Theorem of Calculus

11.3: u-Substitution

12.1: Area between Curves

12.2: Volume of Curves