MATH*1210

University of Guelph

Course Overview

Lessons & Practice

I. Welcome

1. (Review): Integration

1.5hr

1.I. What is Integration?

1.1.1. Review: Sigma Notation6 min

1.1.2. Practice (index

i\neq1

1.1.3. Practice (w/ limits)3 min

1.1.4. Practice (telescoping sum)2 min

1.1.5. Riemann Sums7 min

1.1.6. Practice (left/right sums)2 min

1.1.7. Practice (area)3 min

1.1.8. Practice (area) *Tricky3 min

1.2.1. Definite Integrals 3 min

1.2.2. Practice1 min

1.2.3. Practice *Tricky3 min

1.2.4. Properties of Definite Integrals5 min

1.2.5. Practice1 min

1.3.1. Antiderivatives & Indefinite Integrals6 min

1.3.2. Practice1 min

1.3.3. Practice1 min

1.3.4. Practice (initial condition)2 min

1.4.1. Fundamental Theorem of Calculus 13 min

1.4.2. Practice2 min

1.4.3. Practice (w/ limit)2 min

1.4.4. Fundamental Theorem of Calculus 23 min

1.4.5. Practice2 min

1.4.6. Practice1 min

1.4.7. Practice (absolute values)3 min

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

1.5.2. Practice2 min

1.5.3. Practice3 min

1.5.4. Practice (definite integral)3 min

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

1.5.6. Short-Cut for U-Substitution3 min

1.Q. Integration Quiz18 Qns

2. Complex Numbers

46min

2.1.1. Basics of Complex Numbers4 min

2.1.2. Operations With Complex Numbers9 min

2.1.3. Example5 min

2.1.4. Practice3 min

2.2.1. Polar Form7 min

2.2.2. Geometric Interpretation of Multiplication4 min

2.2.3. Example8 min

2.2.4. Practice1 min

2.2.5. Practice4 min

3. Inverse Functions & Derivatives

58min

4. Hyperbolic, Inverse Hyperbolic Functions, and Derivatives

4min

4.1.1. Hyperbolic Functions and their Derivatives2 min

4.1.2. Example51 sec

4.1.3. Practice59 sec

4.2.1. Inverse Hyperbolic Functions and their Derivatives37 sec

4.2.2. Practice

5. L'Hopital's Rule

21min

5.1.1. L'Hospital's Rule5 min

5.1.2. Example2 min

5.1.3. Practice2 min

5.1.4. Practice5 min

5.1.5. Practice4 min

5.1.6. Practice4 min

6. Integration Techniques (including partial fractions)

2.4hr

6.1.1. Integration by Parts6 min

6.1.2. Practice4 min

6.1.3. Practice (w/

\ln

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

6.2.1. Trigonometric Integrals3 min

6.2.2. Practice (odd power of

\cos x

6.2.3. Practice (odd power of

\sin x

6.2.4. Practice (even powers of

\sin x

\cos x

6.2.5. Practice (even power of

\sec x

6.2.6. Practice (w/

\sec x \tan x

6.2.7. Practice (

\sin (mx)

\sin(nx)

6.2.8. Practice (special case

\sec x

6.2.9. Practice (special case

\sec^3x

6.2.10. Reduction Formula2 min

6.2.11. Practice5 min

6.2.12. Practice3 min

6.3.1. Trigonometric Substitution10 min

6.3.2. Practice6 min

6.3.3. Practice5 min

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

6.4.1. Partial Fractions Decomposition7 min

6.4.2. Practice (linear factors only)4 min

6.4.3. Practice (w/ quadratic factors)7 min

6.4.4. Practice (w/ long division)6 min

6.5.1. Strategies for Integration3 min

6.5.2. Practice (rationalizing substitution)4 min

6.5.3. Practice: Mixed Integrals4 min

6.5.4. Practic6 min

6.5.5. Practice5 min

6.5.6. Practice7 min

6.5.7. Practice7 min

6.Q. Integration Techniques Quiz18 Qns

7. Volumes of Revolution

12min

7.1.1. Volumes of Revolution (Disk/Washer)3 min

7.1.2. Practice (around the x-axis)2 min

7.1.3. Practice (around the y-axis)3 min

7.1.4. Practice (around a line)3 min

8. Improper Integrals

26min

8.1.1. Improper Integrals4 min

8.1.2. Practice (type 1)2 min

8.1.3. Practice (type 1)5 min

8.1.4. Practice (Type 2)5 min

8.2.1. Comparison Theorem for Improper Integrals3 min

8.2.2. Practice (type 1 - converges)3 min

8.2.3. Practice (type 2 - converges)4 min

8.2.4. Practice (type 2 - diverges)

8.Q. Improper Integral Quiz4 Qns

9. Arc Length & Parametric Curves

60min

9.1.1. Arc Length of a Curve3 min

9.1.2. Practice6 min

9.1.3. Practice4 min

9.2.1. Parametric Curves6 min

9.2.2. Practice (Cartesian equations)2 min

9.2.3. Practice (graphs)4 min

9.2.4. Practice (graphs)3 min

9.3.1. Tangents/Derivatives of Parametric Curves2 min

9.3.2. Practice (derivatives)2 min

9.3.3. Practice (horizontal/vertical tangents)5 min

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

9.3.5. Arc Length, Area, and Surface Area2 min

9.3.6. Practice (arc length)3 min

9.3.7. Practice (area)3 min

9.3.8. Practice (surface area)6 min

9.3.9. Practice (surface area)5 min

9.Q. Parametric and polar curves Quiz6 Qns

10. Polar Coordinates

58min

10.1.1. Polar Coordinates7 min

10.1.2. Graphing Polar Curves6 min

10.1.3. Practice (graphs)6 min

10.1.4. Practice (polar coordinates)2 min

10.1.5. Practice (matching graphs)4 min

10.2.1. Tangents/Derivatives of Polar Curves2 min

10.2.2. Practice (derivative)4 min

10.2.3. Practice (horizontal/vertical tangents)7 min

10.2.4. Arc Length, Area Under & Between Curves2 min

10.2.5. Practice (arc length)3 min

10.2.6. Practice (area inside curve)2 min

10.2.7. Practice (area inside curve)4 min

10.2.8. Practice (area between curves)8 min

11. Taylor & Maclaurin Series

1.4hr

11.1.1. Definitions of Power Series9 min

11.1.2. Practice (radius of convergence)2 min

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

11.1.4. Practice: Radius & Interval of Convergence4 min

11.2.1. Representing Functions as Power Series2 min

11.2.2. Practice2 min

11.2.3. Practice2 min

11.2.4. Practice (w/ partial fractions)7 min

11.2.5. Differentiation and Integration of Power Series3 min

11.2.6. Practice (differentiating power series)4 min

11.2.7. Practice (integrating power series)4 min

11.2.8. Practice (integrating power series*)8 min

11.3.1. Taylor and Maclaurin Series6 min

11.3.2. Practice (Taylor series)7 min

11.3.3. Common Maclaurin Series (Memorize!)*5 min

11.3.4. Practice (Maclaurin series)2 min

11.3.5. Practice (Maclaurin series)3 min

11.3.6. Practice (Maclaurin series of an integral)2 min

11.3.7. Practice (evaluating a series*)3 min

11.Q. Power Series Quiz10 Qns

12. Multivariable Functions

36min

12.1.1. Functions of Several Variables5 min

12.1.2. Practice3 min

12.2.1. Partial derivatives6 min

12.2.2. Practice: First Partial derivatives2 min

12.2.3. Practice: Second Partial Derivatives3 min

12.3.1. Chain Rule7 min

12.3.2. Practice: Chain Rule2 min

12.3.3. Practice: Chain Rule2 min

12.3.4. Practice: Chain Rule*3 min

12.3.5. Implicit Differentiation2 min

I Welcome

Free Activity

Welcome to Calculus II!
My name is Corey and I'm the instructor for this course. Feel free to go through this course at your own pace.
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