MAT187H1

U of T

Course Overview

Lessons & Practice

1. Integration Methods

2.1hr

1.1.1. Integration by Parts6 min

1.1.2. Practice4 min

1.1.3. Practice (w/

\ln

)2 min

1.1.4. Practice (w/ exp & trig)6 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. Trigonometric Substitution10 min

1.3.2. Practice6 min

1.3.3. Practice5 min

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

1.4.1. Partial Fractions Decomposition7 min

1.4.2. Practice (linear factors only)4 min

1.4.3. Practice (w/ quadratic factors)7 min

1.4.4. Practice (w/ long division)6 min

1.5.1. The Midpoint Rule1 min

1.5.2. Example2 min

1.5.3. The Trapezoid Rule 1 min

1.5.4. Example2 min

1.5.5. Practice

1.5.6. Simpson's Rule1 min

1.5.7. Example2 min

1.5.8. Practice

1.5.9. Error Bounds for Approximations2 min

1.5.10. Practice

1.5.11. Numerical Integration (Summary)

1.6.1. Improper Integrals4 min

1.6.2. Practice (type 1)2 min

1.6.3. Practice (type 1)5 min

1.6.4. Practice (Type 2)5 min

1.7.1. Comparison Theorem for Improper Integrals3 min

1.7.2. Practice (type 1 - converges)3 min

1.7.3. Practice (type 2 - converges)4 min

1.7.4. Practice (type 2 - diverges)

1.Q. Integration Techniques Quiz18 Qns

2. ODEs

1.1hr

2.1.1. Differential Equations8 min

2.2.1. Separable First Order Differential Equations3 min

2.2.2. Practice (separable DE)2 min

2.2.3. Practice (IVP)3 min

2.2.4. Practice (IVP)3 min

2.2.5. Practice (IVP*)5 min

2.2.6. Practice (separable DE)1 min

2.3.1. Linear First Order Differential Equations7 min

2.3.2. Practice (integrating factor)1 min

2.3.3. Practice (linear DE)3 min

2.3.4. Practice (IVP)3 min

2.3.5. Practice (IVP)4 min

2.4.1. Common DE Applications (Word Problems)

2.4.2. Practice (population)3 min

2.4.3. Practice (population)4 min

2.4.4. Practice (cooling & heating)3 min

2.4.5. Practice (mixing tank)6 min

2.4.6. Practice (mixing tank)8 min

2.5.1. Second-Order Reducible DE

2.5.2. Practice: Dependent Variable Missing

2.5.3. Practice: Independent Variable Missing

2.Q. DE Quiz4 Qns

3. Taylor Series

1.6hr

3.1.1. Definitions of Power Series9 min

3.1.2. Practice (radius of convergence)2 min

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

3.1.4. Practice: Radius & Interval of Convergence4 min

3.2.1. Representing Functions as Power Series2 min

3.2.2. Practice2 min

3.2.3. Practice2 min

3.2.4. Practice (w/ partial fractions)7 min

3.2.5. Differentiation and Integration of Power Series3 min

3.2.6. Practice (differentiating power series)4 min

3.2.7. Practice (integrating power series)4 min

3.2.8. Practice (integrating power series*)8 min

3.3.1. Taylor and Maclaurin Series6 min

3.3.2. Practice (Taylor series)7 min

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

3.3.4. Practice (Maclaurin series)2 min

3.3.5. Practice (Maclaurin series)3 min

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

3.3.7. Practice (evaluating a series*)3 min

3.4.1. Ratio Test2 min

3.4.2. Practice5 min

3.4.3. Practice2 min

3.4.4. Practice (recursive series*)4 min

3.Q. Power Series Quiz10 Qns

4. Vector Valued Calculus

4hr

4.1.1. Parametric Curves6 min

4.1.2. Practice (Cartesian equations)2 min

4.1.3. Practice (graphs)4 min

4.1.4. Practice (graphs)3 min

4.2.1. Tangents/Derivatives of Parametric Curves2 min

4.2.2. Practice (derivatives)2 min

4.2.3. Practice (horizontal/vertical tangents)5 min

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

4.2.5. Arc Length, Area, and Surface Area2 min

4.2.6. Practice (arc length)3 min

4.2.7. Practice (area)3 min

4.2.8. Practice (surface area)6 min

4.2.9. Practice (surface area)5 min

4.3.1. Polar Coordinates7 min

4.3.2. Graphing Polar Curves6 min

4.3.3. Practice (graphs)6 min

4.3.4. Practice (polar coordinates)2 min

4.3.5. Practice (matching graphs)4 min

4.4.1. Tangents/Derivatives of Polar Curves2 min

4.4.2. Practice (derivative)4 min

4.4.3. Practice (horizontal/vertical tangents)7 min

4.4.4. Arc Length, Area Under & Between Curves2 min

4.4.5. Practice (arc length)3 min

4.4.6. Practice (area inside curve)2 min

4.4.7. Practice (area inside curve)4 min

4.4.8. Practice (area between curves)8 min

4.5.1. Vector-Valued Functions5 min

4.5.2. Arc Length6 min

4.5.3. Curvature5 min

4.6.1. Arc Length of a Curve3 min

4.6.2. Wize Concept Clarifier6 min

4.6.3. Practice Question: Arc Length Function4 min

4.7.1. Tangent, Normal, Binormal Vectors 2 min

4.7.2. Example2 min

4.7.3. Example2 min

4.7.4. Practice3 min

4.8.1. What Do We Mean by

\vr(t)

?1 min

4.8.2.

\vr(t)

passing through

P(1,2,-1)

with

\vd = \rowvecth{2}{6}{2}

2 min

4.8.3. A Parameterization for

y = y(x)

2 min

4.8.4. The Tangent Vector5 min

4.8.5. The Length of a Curve9 min

4.8.6. The Normal Vector

4.8.7. Curvature4 min

4.8.8. Curvature5 min

4.8.9. This & That Osculating6 min

4.8.10. This & That Osculating6 min

4.8.11. Practice: The Frenet-Serret Frame34 min

4.8.12. Practice: The Frenet-Serret Frame6 min

4.8.13. Practice:

s

\hat{T}

\hat{N}

\hat{B}

and

\kappa

for

\vr(t)

19 min

4.8.14.

s

\hat{T}

\hat{N}

\hat{B}

\kappa

and

\tau

for

\vr(t)

10 min

4.Q. Parametric and polar curves Quiz6 Qns

Mock Exams

ME.1. Midterm 1 - Mock Assessment15 Qns

ME.2. Midterm 2 - Mock Assessment16 Qns

ME.3. Final Exam - Mock Assessment23 Qns

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ME.2 Midterm 2 - Mock Assessment

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Midterm 2 - Mock Assessment

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