MATH 119
UWaterloo
Course Overview
Lessons & Practice
1. Review: Derivatives
1.3hr1.2.1. Derivative Rules7 min1.2.2. Example: Derivative Rules4 min1.2.3. Product, Quotient, and Chain Rule4 min1.2.4. Example: Product, Quotient, and Chain Rule8 min1.2.5. Practice: Finding a Derivative4 min1.2.6. Practice: Finding a Derivative4 min1.2.7. Practice: Higher Order Derivative6 min1.2.8. Practice: Product Rule*6 min1.2.9. Practice: Chain Rule*6 min
2. Multivariable Functions
1.1hr3. Parametric & Polar Curves
1.8hr3.2.1. Tangents/Derivatives of Parametric Curves2 min3.2.2. Practice (derivatives)2 min3.2.3. Practice (horizontal/vertical tangents)5 min3.2.4. Practice (horizontal/vertical tangents*)6 min3.2.5. Arc Length, Area, and Surface Area2 min3.2.6. Practice (arc length)3 min3.2.7. Practice (area)3 min3.2.8. Practice (surface area)6 min3.2.9. Practice (surface area)5 min
3.4.1. Tangents/Derivatives of Polar Curves2 min3.4.2. Practice (derivative)4 min3.4.3. Practice (horizontal/vertical tangents)7 min3.4.4. Arc Length, Area Under & Between Curves2 min3.4.5. Practice (arc length)3 min3.4.6. Practice (area inside curve)2 min3.4.7. Practice (area inside curve)4 min3.4.8. Practice (area between curves)8 min
4. Integration
1.5hr5. Integration Techniques
2.6hr5.2.1. Trigonometric Integrals3 min5.2.2. Practice (odd power of )3 min5.2.3. Practice (odd power of )3 min5.2.4. Practice (even powers of & )2 min5.2.5. Practice (even power of )4 min5.2.6. Practice (w/ )3 min5.2.7. Practice ( & )1 min5.2.8. Practice (special case )3 min5.2.9. Practice (special case )5 min5.2.10. Reduction Formula2 min5.2.11. Practice5 min5.2.12. Practice3 min
6. Improper Integrals
40min7. Applications of Integrals
1.6hr8. Integral calculus in several variables
3min9. Sequences and Series
2hr9.4.1. Series and Limit Comparison Tests5 min9.4.2. Practice (limit comparison test)2 min9.4.3. Practice (limit comparison test)3 min9.4.4. Practice (telescoping series*)6 min9.4.5. Practice (series comparison test)5 min9.4.6. Practice (series comparison test)2 min9.4.7. Practice (telescoping series*)3 min
10. Power Series
1.4hr10.2.1. Representing Functions as Power Series2 min10.2.2. Practice2 min10.2.3. Practice2 min10.2.4. Practice (w/ partial fractions)7 min10.2.5. Differentiation and Integration of Power Series3 min10.2.6. Practice (differentiating power series)4 min10.2.7. Practice (integrating power series)4 min10.2.8. Practice (integrating power series*)8 min
10.3.1. Taylor and Maclaurin Series6 min10.3.2. Practice (Taylor series)7 min10.3.3. Common Maclaurin Series (Memorize!)*5 min10.3.4. Practice (Maclaurin series)2 min10.3.5. Practice (Maclaurin series)3 min10.3.6. Practice (Maclaurin series of an integral)2 min10.3.7. Practice (evaluating a series*)3 min
11. Differential Equations
1.3hr12. Vector Functions
55min12.1.1. 3D Cooridnate System4 min12.1.2. Vectors7 min12.1.3. Dot Product7 min12.1.4. Cross Product6 min12.1.5. Equations of Lines & Planes10 min12.1.6. Cylinder & Quadric Surface12.1.7. Example: Quadratic Surfaces (1)3 min12.1.8. Example: Quadratic Surfaces (2)2 min12.1.9. Cylindrical & Spherical Coordinates
