1. Pre-Calculus

1.2hr

1.1.1. Trigonometric Functions6 min

1.1.2. Example4 min

1.1.3. Trig Identities2 min

1.1.4. Practice3 min

1.1.5. Practice4 min

1.2.1. Inverse Functions3 min

1.2.2. Example3 min

1.2.3. Practice2 min

1.3.1. Inverse Trigonometric Functions4 min

1.3.2. Example3 min

1.3.3. Practice2 min

1.3.4. Practice2 min

1.4.1. Exponential Functions3 min

1.4.2. Example1 min

1.4.3. Example2 min

1.5.1. Logarithmic Functions4 min

1.5.2. Example3 min

1.5.3. Example:3 min

1.5.4. Practice2 min

1.6.1. Absolute Value Function1 min

1.6.2. Example3 min

1.7.1. Piecewise Functions4 min

1.7.2. Example5 min

1.7.3. Practice3 min

2. Limits & Continuity

1.5hr

2.1.1. Limit Basics2 min

2.1.2. Example1 min

2.2.1. Limit Laws 2 min

2.2.2. Practice1 min

2.3.1. One-Sided Limits2 min

2.3.2. Example: One-Sided Limit2 min

2.3.3. Practice: One-Sided Limits3 min

2.4.1. The Squeeze Theorem2 min

2.4.2. Example2 min

2.4.3. Practice2 min

2.5.1. The Fundamental Trig Limit2 min

2.5.2. Example3 min

2.6.1. Infinite Limits2 min

2.6.2. Example1 min

2.6.3. Example3 min

2.7.1. Limits at Infinity3 min

2.7.2. Example60 sec

2.7.3. Example3 min

2.7.4. Example4 min

2.7.5. Practice 3 min

2.7.6. Practice3 min

2.8.1. Indeterminate Forms50 sec

2.9.1. Computing Limits by Factoring1 min

2.9.2. Example1 min

2.9.3. Practice2 min

2.10.1. Computing Limits by Multiplying by the Conjugate3 min

2.10.2. Example3 min

2.10.3. Practice3 min

2.11.1. Computing Limits by Getting a Common Denominator1 min

2.11.2. Example2 min

2.11.3. Practice4 min

2.12.1. Continuity2 min

2.12.2. Example2 min

2.12.3. Practice4 min

2.13.1. The Intermediate Value Theorem2 min

2.13.2. Example2 min

2.13.3. Practice2 min

2.14.1. The Epsilon Delta Definition of a Limit

2.14.2. Example3 min

2.14.3. Practice

3. Derivatives

2.2hr

3.1.1. The Limit Definition of a Derivative2 min

3.1.2. Example3 min

3.1.3. Practice5 min

3.2.1. Differentiation Laws51 sec

3.3.1. The Power Rule1 min

3.3.2. Example2 min

3.3.3. Practice51 sec

3.4.1. The Product Rule49 sec

3.4.2. Example2 min

3.4.3. Example2 min

3.4.4. Practice2 min

3.5.1. The Quotient Rule1 min

3.5.2. Example2 min

3.5.3. Practice4 min

3.6.1. Derivatives as a Rate of Change2 min

3.6.2. Average Rate of Change46 sec

3.6.3. Example2 min

3.6.4. Practice1 min

3.7.1. Derivatives of Trigonometric Functions1 min

3.8.1. Tangent Lines1 min

3.8.2. Example3 min

3.8.3. Practice2 min

3.9.1. The Chain Rule1 min

3.9.2. Example2 min

3.9.3. Practice3 min

3.10.1. Logarithmic Differentiation2 min

3.10.2. Example2 min

3.10.3. Practice3 min

3.11.1. Higher Order Derivatives2 min

3.11.2. Example3 min

3.11.3. Practice2 min

3.11.4. Practice

3.11.5. Practice2 min

3.12.1. Implicit Differentiation2 min

3.12.2. Example3 min

3.12.3. Example3 min

3.12.4. Practice3 min

3.13.1. Derivatives of Inverse Functions52 sec

3.13.2. Example2 min

3.13.3. Practice3 min

3.14.1. Inverse Trig Derivatives1 min

3.14.2. Example1 min

3.14.3. Practice3 min

3.15.1. Derivatives of Exponential Functions1 min

3.15.2. Example52 sec

3.15.3. Example3 min

3.15.4. Practice1 min

3.16.1. Derivatives of Logarithmic Functions1 min

3.16.2. Example56 sec

3.16.3. Example2 min

3.16.4. Practice2 min

3.16.5. Practice: Log and Ln2 min

3.17.1. Related Rates1 min

3.17.2. Example5 min

3.17.3. Example4 min

3.17.4. Practice2 min

3.17.5. Practice4 min

3.17.6. Practice4 min

4. Applications of Derivatives

1.8hr

4.1.1. Linearization (Linear Approximation)59 sec

4.1.2. Example3 min

4.1.3. Practice3 min

4.1.4. Practice3 min

4.2.1. Differential Equations8 min

4.2.2. Direction Fields/Slope Fields5 min

4.2.3. Practice Question: DE Solution Graphs3 min

4.2.4. Euler's Method (Approximating Solutions)4 min

4.2.5. Practice

4.3.1. Separable First Order Differential Equations3 min

4.3.2. Practice (separable DE)2 min

4.3.3. Practice (IVP)3 min

4.3.4. Practice (IVP)3 min

4.3.5. Practice (IVP*)5 min

4.3.6. Practice (separable DE)1 min

4.4.1. L’Hopital’s Rule2 min

4.4.2. Example2 min

4.4.3. Practice5 min

4.5.1. Critical Points and Extrema2 min

4.5.2. Example

4.5.3. Practice3 min

4.6.1. Extreme Value Theorem1 min

4.7.1. Maximum and Minimum on Closed Intervals2 min

4.7.2. Example4 min

4.7.3. Practice3 min

4.7.4. Practice3 min

4.8.1. Intervals of Increase and Decrease1 min

4.8.2. Example2 min

4.8.3. Practice3 min

4.9.1. 1st and 2nd Derivative Tests3 min

4.9.2. Example7 min

4.9.3. Example

4.9.4. Practice3 min

4.10.1. Optimization1 min

4.10.2. Example4 min

4.10.3. Example4 min

4.10.4. Practice6 min

4.10.5. Practice4 min

5. Definite Integrals & Riemann Sums

56min

5.1.1. Finite Sums & Summation Notation3 min

5.1.2. Example5 min

5.1.3. Practice4 min

5.1.4. Practice4 min

5.2.1. Approximating Areas & Riemann Sums 3 min

5.2.2. Example4 min

5.2.3. Practice3 min

5.3.1. The Definite Integrals & Area Under a Curve2 min

5.3.2. Example7 min

5.3.3. Practice2 min

5.3.4. Practice12 min

5.4.1. Properties of the Definite Integral2 min

5.4.2. Practice2 min

5.4.3. Practice2 min

6. Antiderivatives

1.4hr

6.1.1. Antiderivatives (Indefinite Integral)3 min

6.2.1. Antiderivatives (Indefinite Integral) of Trig Functions4 min

6.2.2. Example1 min

6.2.3. Practice1 min

6.2.4. Practice1 min

6.3.1. Antiderivatives (Indefinite Integrals) of Inverse Trig Functions2 min

6.3.2. Example1 min

6.3.3. Practice1 min

6.4.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

6.4.2. Example42 sec

6.4.3. Practice1 min

6.4.4. Practice2 min

6.5.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

2 min

6.5.2. Example2 min

6.5.3. Practice1 min

6.6.1. Initial Conditions2 min

6.6.2. Example2 min

6.6.3. Practice5 min

6.7.1. Fundamental Theorem of Calculus - Part I2 min

6.8.1. Fundamental Theorem of Calculus - Part 21 min

6.8.2. Example2 min

6.8.3. Example

6.8.4. Practice 4 min

6.8.5. Practice3 min

6.8.6. Practice1 min

6.9.1. U-Substitution (Integration by Substitution)6 min

6.9.2. Practice2 min

6.9.3. Practice3 min

6.9.4. Practice (definite integral)3 min

6.9.5. Practice (w/ back-sub)4 min

6.9.6. Short-Cut for U-Substitution3 min

Mock Exams

ME.1. Term Test 2 - Mock Assessment30 Qns

ME.2. Term Test 1 - Mock Assessment20 Qns

ME.3. Final Exam - Mock Assessment17 Qns

MAT186H1

Course Overview

Grade Boosters

1. Pre-Calculus

2. Limits & Continuity

3. Derivatives

4. Applications of Derivatives

5. Definite Integrals & Riemann Sums

6. Antiderivatives

Mock Exams

Term Test 2 Overview

Course Notes