MATH 101A

UBC

Course Overview

Lessons & Practice

I. Welcome

1. Integration

2hr

1.1.1. Finite Sums & Summation Notation3 min

1.1.2. Example5 min

1.1.3. Practice4 min

1.1.4. Practice4 min

1.2.1. Approximating Areas & Riemann Sums 3 min

1.2.2. Example4 min

1.2.3. Practice3 min

1.3.1. The Definite Integrals & Area Under a Curve2 min

1.3.2. Example7 min

1.3.3. Practice2 min

1.3.4. Practice12 min

1.4.1. Properties of the Definite Integral2 min

1.4.2. Practice2 min

1.4.3. Practice2 min

1.5.1. Computing Definite Integrals Geometrically44 sec

1.5.2. Example1 min

1.5.3. Practice1 min

1.6.1. Fundamental Theorem of Calculus - Part I2 min

1.7.1. Fundamental Theorem of Calculus - Part 21 min

1.7.2. Example2 min

1.7.3. Example

1.7.4. Practice 4 min

1.7.5. Practice3 min

1.7.6. Practice1 min

1.8.1. Integration by Substitution2 min

1.8.2. Example4 min

1.8.3. Example3 min

1.8.4. Example (w/ Back-Substitution)4 min

1.8.5. Practice

1.8.6. Practice

1.8.7. Practice

1.8.8. Practice (w/ Back-Substitution)

2. Integration Techniques

2.6hr

2.1.1. Trigonometric Integrals3 min

2.1.2. Practice (odd power of

\cos x

)3 min

2.1.3. Practice (odd power of

\sin x

)3 min

2.1.4. Practice (even powers of

\sin x

\cos x

)2 min

2.1.5. Practice (even power of

\sec x

)4 min

2.1.6. Practice (w/

\sec x \tan x

)3 min

2.1.7. Practice (

\sin (mx)

\sin(nx)

)1 min

2.1.8. Practice (special case

\sec x

)3 min

2.1.9. Practice (special case

\sec^3x

)5 min

2.1.10. Reduction Formula2 min

2.1.11. Practice5 min

2.1.12. Practice3 min

2.2.1. Trigonometric Substitution10 min

2.2.2. Practice6 min

2.2.3. Practice5 min

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

2.3.1. Partial Fractions Decomposition7 min

2.3.2. Practice (linear factors only)4 min

2.3.3. Practice (w/ quadratic factors)7 min

2.3.4. Practice (w/ long division)6 min

2.4.1. Integration by Parts6 min

2.4.2. Practice4 min

2.4.3. Practice (w/

\ln

)2 min

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

2.5.1. Strategies for Integration3 min

2.5.2. Practice (rationalizing substitution)4 min

2.5.3. Practice: Mixed Integrals4 min

2.6.1. The Midpoint Rule1 min

2.6.2. Example2 min

2.6.3. The Trapezoid Rule 1 min

2.6.4. Example2 min

2.6.5. Practice

2.6.6. Simpson's Rule1 min

2.6.7. Example2 min

2.6.8. Practice

2.6.9. Error Bounds for Approximations2 min

2.6.10. Practice

2.6.11. Numerical Integration (Summary)

2.Q. Integration Techniques Quiz18 Qns

3. Volumes

28min

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

4. Improper Integrals

40min

4.1.1. L'Hospital's Rule5 min

4.1.2. Practice2 min

4.1.3. Practice4 min

4.1.4. Practice4 min

4.2.1. Improper Integrals4 min

4.2.2. Practice (type 1)2 min

4.2.3. Practice (type 1)5 min

4.2.4. Practice (Type 2)5 min

4.3.1. Comparison Theorem for Improper Integrals3 min

4.3.2. Practice (type 1 - converges)3 min

4.3.3. Practice (type 2 - converges)4 min

4.3.4. Practice (type 2 - diverges)

4.Q. Improper Integral Quiz4 Qns

5. Application of Integrals - Probability

15min

5.1.1. Distribution Functions4 min

5.1.2. Practice: PDF3 min

5.1.3. Practice: CDF2 min

5.1.4. Mean, Median, and Variance3 min

5.1.5. Practice2 min

5.1.6. Practice: Median1 min

6. Sequences and Series

2hr

6.1.1. Sequences8 min

6.1.2. Series7 min

6.1.3. Practice (Partial sums)2 min

6.1.4. Practice (Geometric series)2 min

6.1.5. Practice (Geometric series)3 min

6.1.6. Practice: Series Application6 min

6.1.7. How to Test if a Series Converges?

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

6.3.1. Integral Test1 min

6.3.2. Practice: Integral Test6 min

6.3.3. Practice: Integral Test5 min

6.4.1. Series and Limit Comparison Tests5 min

6.4.2. Practice (limit comparison test)2 min

6.4.3. Practice (limit comparison test)3 min

6.4.4. Practice (telescoping series*)6 min

6.4.5. Practice (series comparison test)5 min

6.4.6. Practice (series comparison test)2 min

6.4.7. Practice (telescoping series*)3 min

6.5.1. Absolute Convergence Test3 min

6.5.2. Practice5 min

6.5.3. Alternating Series Test2 min

6.5.4. Practice: AST5 min

6.6.1. Ratio Test2 min

6.6.2. Practice5 min

6.6.3. Practice2 min

6.6.4. Practice (recursive series*)4 min

6.7.1. Root Test1 min

6.7.2. Practice3 min

6.7.3. Practice: Root Test4 min

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

6.Q. Sequences and Series Quiz13 Qns

7. Power Series

1.4hr

7.1.1. Definitions of Power Series9 min

7.1.2. Practice (radius of convergence)2 min

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

7.1.4. Practice: Radius & Interval of Convergence4 min

7.2.1. Representing Functions as Power Series2 min

7.2.2. Practice2 min

7.2.3. Practice2 min

7.2.4. Practice (w/ partial fractions)7 min

7.2.5. Differentiation and Integration of Power Series3 min

7.2.6. Practice (differentiating power series)4 min

7.2.7. Practice (integrating power series)4 min

7.2.8. Practice (integrating power series*)8 min

7.3.1. Taylor and Maclaurin Series6 min

7.3.2. Practice (Taylor series)7 min

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

7.3.4. Practice (Maclaurin series)2 min

7.3.5. Practice (Maclaurin series)3 min

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

7.3.7. Practice (evaluating a series*)3 min

7.Q. Power Series Quiz10 Qns

8. Differential Equations

1.2hr

8.1.1. Differential Equations8 min

8.1.2. Direction Fields/Slope Fields5 min

8.1.3. Practice Question: DE Solution Graphs3 min

8.2.1. Separable First Order Differential Equations3 min

8.2.2. Practice (separable DE)2 min

8.2.3. Practice (IVP)3 min

8.2.4. Practice (IVP)3 min

8.2.5. Practice (IVP*)5 min

8.2.6. Practice (separable DE)1 min

8.3.1. Linear First Order Differential Equations7 min

8.3.2. Practice (integrating factor)1 min

8.3.3. Practice (linear DE)3 min

8.3.4. Practice (IVP)3 min

8.3.5. Practice (IVP)4 min

8.4.1. Exponential Growth and Decay3 min

8.4.2. Example4 min

8.4.3. Example5 min

8.4.4. Practice5 min

8.4.5. Practice (population)3 min

8.4.6. Practice (population)4 min

8.5.1. Second-Order Reducible DE

8.5.2. Practice: Dependent Variable Missing

8.5.3. Practice: Independent Variable Missing

8.Q. DE Quiz4 Qns

Mock Exams

ME.1. Test 1 - Mock Assessment7 Qns

ME.2. Test 2 - Mock Assessment15 Qns

ME.3. Final Exam - Mock Assessment25 Qns

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ME.3 Final Exam - Mock Assessment

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Final Exam - Mock Assessment

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