MATH 267

U of C

Course Overview

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Lessons & Practice

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1. (Review): Derivatives & Integrals

60min

1.1.1. Derivative Rules7 min

1.1.2. Example: Derivative Rules4 min

1.1.3. Product, Quotient, and Chain Rule4 min

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

1.1.5. Practice: Finding a Derivative4 min

1.1.6. Practice: Finding a Derivative4 min

1.1.7. Practice: Higher Order Derivative6 min

1.1.8. Practice: Product Rule*6 min

1.1.9. Practice: Chain Rule*6 min

1.2.1. Antiderivatives & Indefinite Integrals6 min

1.2.2. Practice1 min

1.2.3. Practice1 min

1.2.4. Practice (initial condition)2 min

2. Integration Techniques

2.7hr

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.Q. Integration Techniques Quiz18 Qns

3. Applications of Integrals

53min

3.1.1. Volumes - Cross Sections Method3 min

3.1.2. Practice4 min

3.1.3. Practice3 min

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

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

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

3.2.4. Practice (around a line)3 min

3.3.1. Volumes of Revolution (Cylindrical Shells)4 min

3.3.2. Practice2 min

3.4.1. Arc Length of a Curve3 min

3.4.2. Practice6 min

3.4.3. Practice4 min

3.5.1. Surface Area of Revolution1 min

3.5.2. Example5 min

3.5.3. Practice

3.6.1. Surface Area of Revolution1 min

3.6.2. Example5 min

3.6.3. Practice

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

1.4hr

5.1.1. Definitions of Power Series9 min

5.1.2. Practice (radius of convergence)2 min

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

5.1.4. Practice: Radius & Interval of Convergence4 min

5.2.1. Representing Functions as Power Series2 min

5.2.2. Practice2 min

5.2.3. Practice2 min

5.2.4. Practice (w/ partial fractions)7 min

5.2.5. Differentiation and Integration of Power Series3 min

5.2.6. Practice (differentiating power series)4 min

5.2.7. Practice (integrating power series)4 min

5.2.8. Practice (integrating power series*)8 min

5.3.1. Taylor and Maclaurin Series6 min

5.3.2. Practice (Taylor series)7 min

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

5.3.4. Practice (Maclaurin series)2 min

5.3.5. Practice (Maclaurin series)3 min

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

5.3.7. Practice (evaluating a series*)3 min

5.Q. Power Series Quiz10 Qns

6. Multivariable Functions

36min

6.1.1. Functions of Several Variables5 min

6.1.2. Practice3 min

6.2.1. Partial derivatives6 min

6.2.2. Practice: First Partial derivatives2 min

6.2.3. Practice: Second Partial Derivatives3 min

6.3.1. Chain Rule7 min

6.3.2. Practice: Chain Rule2 min

6.3.3. Practice: Chain Rule2 min

6.3.4. Practice: Chain Rule*3 min

6.3.5. Implicit Differentiation2 min

7. Polar Coordinates & Curves

58min

7.1.1. Polar Coordinates7 min

7.1.2. Graphing Polar Curves6 min

7.1.3. Practice (graphs)6 min

7.1.4. Practice (polar coordinates)2 min

7.1.5. Practice (matching graphs)4 min

7.2.1. A note about this section

7.2.2. Tangents/Derivatives of Polar Curves2 min

7.2.3. Practice (derivative)4 min

7.2.4. Practice (horizontal/vertical tangents)7 min

7.2.5. Arc Length, Area Under & Between Curves2 min

7.2.6. Practice (arc length)3 min

7.2.7. Practice (area inside curve)2 min

7.2.8. Practice (area inside curve)4 min

7.2.9. Practice (area between curves)8 min

8. Multiple Integrals

3min

8.1.1. Double Integration (rectangular)

8.1.2. Practice: Double integration

8.1.3. Practice: Changing the order of integration

8.1.4. Practice: Changing the order of integration

8.1.5. Interpretation of a Double Integral

8.1.6. Practice: Volume under a surface

8.2.1. Double Integration (polar)

8.2.2. Practice: Double integration (polar)

8.3.1. Triple Integration (rectangular)

8.3.2. Practice: Triple integration (rectangular)

8.3.3. Practice: Triple integration (rectangular)

8.4.1. Cylindrical coordinates

8.4.2. Triple Integration (cylindrical)

8.4.3. Practice: Cylindrical coordinates

8.4.4. Example: Triple integration (cylindrical)

8.4.5. Practice: Triple integration (cylindrical)

8.5.1. Spherical coordinates

8.5.2. Triple Integration (spherical)

8.5.3. Practice: Triple integration (spherical)

8.5.4. Practice: Triple integration (spherical)

8.5.5. Practice: Triple integration (spherical)3 min

8.6.1. Multiple Integrals Quiz15 Qns

Mock Exams

ME.1. Term Exam 1 - Mock Assessment22 Qns

ME.2. Term Exam 2 - Mock Assessment15 Qns

ME.3. Final Exam - Mock Assessment24 Qns

MATH 267 Grade Boosters

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