MATH 118

UWaterloo

Course Overview

Lessons & Practice

I. Welcome

1. Review: Derivatives

1.3hr

1.1.1. Interpretation of Derivatives8 min

1.1.2. Practice: Definition of Derivative6 min

1.1.3. Practice: Differentiability4 min

1.2.1. Derivative Rules7 min

1.2.2. Example: Derivative Rules4 min

1.2.3. Product, Quotient, and Chain Rule4 min

1.2.4. Example: Product, Quotient, and Chain Rule8 min

1.2.5. Practice: Finding a Derivative4 min

1.2.6. Practice: Finding a Derivative4 min

1.2.7. Practice: Higher Order Derivative6 min

1.2.8. Practice: Product Rule*6 min

1.2.9. Practice: Chain Rule*6 min

1.3.1. Tangent and Normal Lines4 min

1.3.2. Practice: Equation of Tangent Line

1.3.3. Practice: Slope of a Normal Line3 min

1.4.1. Implicit Differentiation1 min

1.4.2. Practice: Implicit differentiation4 min

2. Integration Techniques

4hr

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

2.1.2. Practice2 min

2.1.3. Practice3 min

2.1.4. Practice (definite integral)3 min

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

2.1.6. Short-Cut for U-Substitution3 min

2.2.1. Integration by Parts6 min

2.2.2. Practice4 min

2.2.3. Practice (w/

\ln

2.2.4. Practice (w/ exp & trig)6 min

2.3.1. Trigonometric Integrals3 min

2.3.2. Practice (odd power of

\cos x

2.3.3. Practice (odd power of

\sin x

2.3.4. Practice (even powers of

\sin x

\cos x

2.3.5. Practice (even power of

\sec x

2.3.6. Practice (w/

\sec x \tan x

2.3.7. Practice (

\sin (mx)

\sin(nx)

2.3.8. Practice (special case

\sec x

2.3.9. Practice (special case

\sec^3x

2.3.10. Reduction Formula2 min

2.3.11. Practice5 min

2.3.12. Practice3 min

2.4.1. Trigonometric Substitution10 min

2.4.2. Practice6 min

2.4.3. Practice5 min

2.4.4. Practice (w/ completing the square)6 min

2.5.1. Partial Fractions Decomposition7 min

2.5.2. Practice (linear factors only)4 min

2.5.3. Practice (w/ quadratic factors)7 min

2.5.4. Practice (w/ long division)6 min

2.6.1. Strategies for Integration3 min

2.6.2. Practice (rationalizing substitution)4 min

2.6.3. Practice: Mixed Integrals4 min

2.6.4. Practic6 min

2.6.5. Practice5 min

2.6.6. Practice7 min

2.6.7. Practice7 min

2.7.1. L'Hospital's Rule5 min

2.7.2. Practice2 min

2.7.3. Practice4 min

2.7.4. Practice4 min

2.8.1. Improper Integrals4 min

2.8.2. Practice (type 1)2 min

2.8.3. Practice (type 1)5 min

2.8.4. Practice (Type 2)5 min

2.9.1. Comparison Theorem for Improper Integrals3 min

2.9.2. Practice (type 1 - converges)3 min

2.9.3. Practice (type 2 - converges)4 min

2.9.4. Practice (type 2 - diverges)

2.10.1. The Midpoint Rule1 min

2.10.2. Example2 min

2.10.3. The Trapezoid Rule 1 min

2.10.4. Example2 min

2.10.5. Practice

2.10.6. Simpson's Rule1 min

2.10.7. Example2 min

2.10.8. Practice

2.10.9. Error Bounds for Approximations2 min

2.10.10. Practice

2.10.11. Numerical Integration (Summary)

2.Q. Integration Techniques Quiz18 Qns

3. Differential Equations

1.3hr

3.1.1. Differential Equations8 min

3.1.2. Direction Fields/Slope Fields5 min

3.1.3. Practice Question: DE Solution Graphs3 min

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

3.1.5. Practice

3.2.1. Separable First Order Differential Equations3 min

3.2.2. Practice (separable DE)2 min

3.2.3. Practice (IVP)3 min

3.2.4. Practice (IVP)3 min

3.2.5. Practice (IVP*)5 min

3.2.6. Practice (separable DE)1 min

3.3.1. Linear First Order Differential Equations7 min

3.3.2. Practice (integrating factor)1 min

3.3.3. Practice (linear DE)3 min

3.3.4. Practice (IVP)3 min

3.3.5. Practice (IVP)4 min

3.4.1. Common DE Applications (Word Problems)

3.4.2. Practice (population)3 min

3.4.3. Practice (population)4 min

3.4.4. Practice (cooling & heating)3 min

3.4.5. Practice (mixing tank)6 min

3.4.6. Practice (mixing tank)8 min

3.5.1. Second-Order Reducible DE

3.5.2. Practice: Dependent Variable Missing

3.5.3. Practice: Independent Variable Missing

3.Q. DE Quiz4 Qns

4. Sequences and Series

2hr

4.1.1. Sequences8 min

4.1.2. Series7 min

4.1.3. Practice (Partial sums)2 min

4.1.4. Practice (Geometric series)2 min

4.1.5. Practice (Geometric series)3 min

4.1.6. Practice: Series Application6 min

4.1.7. How to Test if a Series Converges?

4.2.1. Test of Divergence (nth Term Limit Test)2 min

4.2.2. Practice2 min

4.2.3. Practice1 min

4.2.4. Practice3 min

4.2.5. Practice3 min

4.3.1. Integral Test1 min

4.3.2. Practice: Integral Test6 min

4.3.3. Practice: Integral Test5 min

4.4.1. Series and Limit Comparison Tests5 min

4.4.2. Practice (limit comparison test)2 min

4.4.3. Practice (limit comparison test)3 min

4.4.4. Practice (telescoping series*)6 min

4.4.5. Practice (series comparison test)5 min

4.4.6. Practice (series comparison test)2 min

4.4.7. Practice (telescoping series*)3 min

4.5.1. Absolute Convergence Test3 min

4.5.2. Practice5 min

4.5.3. Alternating Series Test2 min

4.5.4. Practice: AST5 min

4.6.1. Ratio Test2 min

4.6.2. Practice5 min

4.6.3. Practice2 min

4.6.4. Practice (recursive series*)4 min

4.7.1. Root Test1 min

4.7.2. Practice3 min

4.7.3. Practice: Root Test4 min

4.8.1. How to Pick Which Convergence Test to Use?6 min

4.Q. Sequences and Series Quiz13 Qns

5. Power Series

1.1hr

5.1.1. Taylor and Maclaurin Series6 min

5.1.2. Practice (Taylor series)7 min

5.2.1. Definitions of Power Series9 min

5.2.2. Practice (radius of convergence)2 min

5.2.3. Practice (radius & interval of convergence)7 min

5.2.4. Practice: Radius & Interval of Convergence4 min

5.3.1. Representing Functions as Power Series2 min

5.3.2. Practice2 min

5.3.3. Practice2 min

5.3.4. Practice (w/ partial fractions)7 min

5.3.5. Differentiation and Integration of Power Series3 min

5.3.6. Practice (differentiating power series)4 min

5.3.7. Practice (integrating power series)4 min

5.3.8. Practice (integrating power series*)8 min

5.Q. Power Series Quiz10 Qns

6. Parametric & Polar Curves

1.8hr

6.1.1. Parametric Curves6 min

6.1.2. Practice (Cartesian equations)2 min

6.1.3. Practice (graphs)4 min

6.1.4. Practice (graphs)3 min

6.2.1. Tangents/Derivatives of Parametric Curves2 min

6.2.2. Practice (derivatives)2 min

6.2.3. Practice (horizontal/vertical tangents)5 min

6.2.4. Practice (horizontal/vertical tangents*)6 min

6.2.5. Arc Length, Area, and Surface Area2 min

6.2.6. Practice (arc length)3 min

6.2.7. Practice (area)3 min

6.2.8. Practice (surface area)6 min

6.2.9. Practice (surface area)5 min

6.3.1. Polar Coordinates7 min

6.3.2. Graphing Polar Curves6 min

6.3.3. Practice (graphs)6 min

6.3.4. Practice (polar coordinates)2 min

6.3.5. Practice (matching graphs)4 min

6.4.1. Tangents/Derivatives of Polar Curves2 min

6.4.2. Practice (derivative)4 min

6.4.3. Practice (horizontal/vertical tangents)7 min

6.4.4. Arc Length, Area Under & Between Curves2 min

6.4.5. Practice (arc length)3 min

6.4.6. Practice (area inside curve)2 min

6.4.7. Practice (area inside curve)4 min

6.4.8. Practice (area between curves)8 min

6.Q. Parametric and polar curves Quiz6 Qns

Mock Exam

ME.1. Midterm32 Qns

I Welcome

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