MAT 1322

uOttawa

Course Overview

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Lessons & Practice

I. Welcome

1. (MAT 1320 Review): Integration

3hr

1.1.1. Antiderivatives & Indefinite Integrals6 min

1.1.2. Practice1 min

1.1.3. Practice1 min

1.1.4. Practice (initial condition)2 min

1.1.5. Practice2 min

1.1.6. Practice1 min

1.1.7. Practice (absolute values)3 min

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

1.2.2. Practice2 min

1.2.3. Practice3 min

1.2.4. Practice (definite integral)3 min

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

1.2.6. Short-Cut for U-Substitution3 min

1.3.1. Integration by Parts6 min

1.3.2. Practice4 min

1.3.3. Practice (w/

\ln

)2 min

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

1.4.1. Trigonometric Integrals3 min

1.4.2. Practice (odd power of

\cos x

)3 min

1.4.3. Practice (odd power of

\sin x

)3 min

1.4.4. Practice (even powers of

\sin x

\cos x

)2 min

1.4.5. Practice (even power of

\sec x

)4 min

1.4.6. Practice (w/

\sec x \tan x

)3 min

1.4.7. Practice (

\sin (mx)

\sin(nx)

)1 min

1.4.8. Practice (special case

\sec x

)3 min

1.4.9. Practice (special case

\sec^3x

)5 min

1.4.10. Reduction Formula2 min

1.4.11. Practice5 min

1.4.12. Practice3 min

1.5.1. Trigonometric Substitution10 min

1.5.2. Practice6 min

1.5.3. Practice5 min

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

1.6.1. Partial Fractions Decomposition7 min

1.6.2. Practice (linear factors only)4 min

1.6.3. Practice (w/ quadratic factors)7 min

1.6.4. Practice (w/ long division)6 min

1.7.1. Strategies for Integration3 min

1.7.2. Practice (rationalizing substitution)4 min

1.7.3. Practice: Mixed Integrals4 min

1.Q. Integration Techniques Quiz18 Qns

2. Improper Integrals

40min

2.1.1. Improper Integrals4 min

2.1.2. Practice (type 1)2 min

2.1.3. Practice (type 1)5 min

2.1.4. Practice (Type 2)5 min

2.2.1. Comparison Theorem for Improper Integrals3 min

2.2.2. Practice (type 1 - converges)3 min

2.2.3. Practice (type 2 - converges)4 min

2.2.4. Practice (type 2 - diverges)

2.3.1. L'Hospital's Rule5 min

2.3.2. Practice2 min

2.3.3. Practice4 min

2.3.4. Practice4 min

2.Q. Improper Integral Quiz4 Qns

3. Applications of Integrals

1.4hr

3.1.1. Area between Curves3 min

3.1.2. Practice4 min

3.1.3. Practice3 min

3.1.4. Practice (multiple regions)4 min

3.2.1. Volumes - Cross Sections Method3 min

3.2.2. Practice4 min

3.2.3. Practice3 min

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

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

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

3.3.4. Practice (around a line)3 min

3.4.1. Volumes of Revolution (Cylindrical Shells)4 min

3.4.2. Practice2 min

3.5.1. Arc Length of a Curve3 min

3.5.2. Practice6 min

3.5.3. Practice4 min

3.6.1. Average value of a function3 min

3.6.2. Example2 min

3.6.3. Practice2 min

3.6.4. Displacement, Velocity, and Acceleration4 min

3.6.5. Rates of Change and Integrals3 min

3.7.1. Mass and Density60 sec

3.9.1. Pressure and Force1 min

3.9.2. Example

3.9.3. Practice3 min

3.Q. Applications of Integration Quiz7 Qns

4. Differential Equations

1.3hr

4.1.1. Differential Equations8 min

4.1.2. Practice (population)4 min

4.1.3. Direction Fields/Slope Fields5 min

4.1.4. Practice Question: DE Solution Graphs3 min

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

4.1.6. Practice

4.2.1. Separable First Order Differential Equations3 min

4.2.2. Practice (separable DE)2 min

4.2.3. Practice (IVP)3 min

4.2.4. Practice (IVP)3 min

4.2.5. Practice (IVP*)5 min

4.2.6. Practice (separable DE)1 min

4.2.7. Practice (population)3 min

4.3.1. A Note About This Section

4.3.2. Linear First Order Differential Equations7 min

4.3.3. Practice (integrating factor)1 min

4.3.4. Practice (linear DE)3 min

4.3.5. Practice (IVP)3 min

4.3.6. Practice (IVP)4 min

4.3.7. Practice (cooling & heating)3 min

4.3.8. Practice (mixing tank)6 min

4.3.9. Practice (mixing tank)8 min

5. Sequences and Series

2hr

5.1.1. Sequences8 min

5.1.2. Series7 min

5.1.3. Practice (Partial sums)2 min

5.1.4. Practice (Geometric series)2 min

5.1.5. Practice (Geometric series)3 min

5.1.6. Practice: Series Application6 min

5.1.7. How to Test if a Series Converges?

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

5.3.1. Integral Test1 min

5.3.2. Practice: Integral Test6 min

5.3.3. Practice: Integral Test5 min

5.4.1. Series and Limit Comparison Tests5 min

5.4.2. Practice (limit comparison test)2 min

5.4.3. Practice (limit comparison test)3 min

5.4.4. Practice (telescoping series*)6 min

5.4.5. Practice (series comparison test)5 min

5.4.6. Practice (series comparison test)2 min

5.4.7. Practice (telescoping series*)3 min

5.5.1. Absolute Convergence Test3 min

5.5.2. Practice5 min

5.5.3. Alternating Series Test2 min

5.5.4. Practice: AST5 min

5.6.1. Ratio Test2 min

5.6.2. Practice5 min

5.6.3. Practice2 min

5.6.4. Practice (recursive series*)4 min

5.7.1. Root Test1 min

5.7.2. Practice3 min

5.7.3. Practice: Root Test4 min

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

5.Q. Sequences and Series Quiz13 Qns

6. Power Series

1.4hr

6.1.1. Definitions of Power Series9 min

6.1.2. Practice (radius of convergence)2 min

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

6.1.4. Practice: Radius & Interval of Convergence4 min

6.2.1. Representing Functions as Power Series2 min

6.2.2. Practice2 min

6.2.3. Practice2 min

6.2.4. Practice (w/ partial fractions)7 min

6.2.5. Differentiation and Integration of Power Series3 min

6.2.6. Practice (differentiating power series)4 min

6.2.7. Practice (integrating power series)4 min

6.2.8. Practice (integrating power series*)8 min

6.3.1. Taylor and Maclaurin Series6 min

6.3.2. Practice (Taylor series)7 min

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

6.3.4. Practice (Maclaurin series)2 min

6.3.5. Practice (Maclaurin series)3 min

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

6.3.7. Practice (evaluating a series*)3 min

6.Q. Power Series Quiz10 Qns

7. Multivariable Functions

48min

7.1.1. Functions of Several Variables5 min

7.1.2. Practice3 min

7.2.1. Partial derivatives6 min

7.2.2. Practice: First Partial derivatives2 min

7.2.3. Practice: Second Partial Derivatives3 min

7.3.1. Tangent plane3 min

7.3.2. Practice: Tangent Plane

7.3.3. Linear (Tangent Plane) Approximation3 min

7.3.4. Practice: Linear approximation

7.4.1. Chain Rule7 min

7.4.2. Practice: Chain Rule2 min

7.4.3. Practice: Chain Rule2 min

7.4.4. Practice: Chain Rule*3 min

7.4.5. Implicit Differentiation2 min

7.5.1. Gradient and directional derivative7 min

7.5.2. Practice: Gradient and directional derivative

Mock Exams

ME.1. Midterm Exam 1 - Mock Assessment19 Qns

ME.2. Midterm Exam 2 - Mock Assessment13 Qns

ME.3. Final Exam - Mock Assessment16 Qns

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ME.3 Final Exam - Mock Assessment

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