MATH 277

U of C

Course Overview

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Lessons & Practice

1. Vector Functions, Curvature and Torsion

59min

1.1.1. Single variable vector functions1 min

1.1.2. Derivative rules for vector functions2 min

1.1.3. Example: Derivative of a vector function2 min

1.1.4. Example: Derivative of a vector function1 min

1.2.1. Motion2 min

1.2.2. Example: Motion7 min

1.2.3. Rocket launch2 min

1.2.4. Example: Rocket launch2 min

1.3.1. Curvature and torsion9 min

1.3.2. Example: Curvature and torsion11 min

1.3.3. Banking a turn3 min

1.3.4. Example: Banking a turn1 min

1.4.1. Parametric equations3 min

1.4.2. Suggestions for parametrization8 min

1.4.3. Example: Tangent line3 min

1.4.4. Example: Parametrization2 min

1.4.5. Example: Parametrization1 min

2. Differential Calculus in Several Variables

2hr

2.I. Higher order partial derivatives

2.1.1. Domain of multivariable functions5 min

2.1.2. Conic sections5 min

2.1.3. Example: Domain of multivariable functions4 min

2.1.4. Example: Domain of multivariable functions2 min

2.1.5. Example: Domain of multivariable functions2 min

2.1.6. Example: Limits4 min

2.2.1. Traces (level curves)2 min

2.2.2. Example: Level curves2 min

2.2.3. Example: Level curves3 min

2.2.4. Example: Level curves5 min

2.3.1. Quadric surfaces4 min

2.3.2. Conic sections5 min

2.3.3. Example: Quadric surfaces4 min

2.3.4. Example: Quadric surfaces1 min

2.3.5. Example: Quadric surfaces1 min

2.3.6. Example: Quadric surfaces54 sec

2.3.7. Example: Quadric surfaces45 sec

2.3.8. Example: Quadric surfaces

2.3.9. Example: Quadric surfaces

2.3.10. Example: Quadric surfaces

2.3.11. Example: Quadric surfaces2 min

2.4.1. Partial derivatives2 min

2.4.2. Example: Partial derivatives3 min

2.4.3. Example: Partial derivatives33 sec

2.4.4. Example: Partial derivatives

2.5.1. Higher order partial derivatives3 min

2.5.2. Example: Higher order partial derivatives3 min

2.5.3. Example: Higher order partial derivatives3 min

2.5.4. Example: Higher order partial derivatives1 min

2.6.1. Chain Rule1 min

2.6.2. Example: Chain Rule3 min

2.6.3. Example: Chain Rule3 min

2.6.4. Example: Chain Rule4 min

2.6.5. Example: Chain Rule3 min

2.7.1. Linear approximation1 min

2.7.2. Example: Linear approximation

2.7.3. Example: Linear approximation2 min

2.7.4. Example: Linear approximation1 Qn

2.7.5. Example: Linear approximation4 min

2.7.6. Example: Linear approximation1 min

2.8.1. Differentials2 min

2.8.2. Example: Differentials2 min

2.8.3. Example: Differentials

2.8.4. Example: Differentials

2.9.1. Gradient and directional derivative3 min

2.9.2. Example: Gradient and directional derivative2 min

2.9.3. Example: Gradient and directional derivative1 min

2.9.4. Example: Gradient and directional derivative3 min

2.10.1. Implicit partial differentiation4 min

2.10.2. Example: Implicit partial differentiation56 sec

2.10.3. Example: Implicit partial differentiation1 Qn

2.10.4. Example: Implicit partial differentiation

2.10.5. Systems of implicit equations and the Jacobian4 min

2.10.6. Example: Systems of implicit equations and the Jacobian3 min

2.10.7. Example: Systems of implicit equations and the Jacobian

2.11.1. Tangent plane2 min

2.11.2. Example: Tangent plane2 min

2.12.1. Exam multivariable differentiation (Exam 1)7 Qns

2.12.2. Exam multivariable differentiation (Exam 2)7 Qns

2.12.3. Exam multivariable differentiation (Exam 3)7 Qns

2.12.4. Exam multivariable differentiation (Exam 4)6 Qns

2.12.5. Exam domain and traces (Exam 1)7 Qns

2.12.6. Exam domain and traces (Exam 2)7 Qns

2.12.7. Exam domain and traces (Exam 3)7 Qns

2.12.8. Exam domain and traces (Exam 4)6 Qns

2.12.9. Exam domain and traces (Exam 5)6 Qns

3. Applications of Partial Derivatives

27min

3.1.1. Extreme Values3 min

3.1.2. Extreme Values2 min

3.1.3. Extreme Values4 min

3.1.4. Extreme Values2 min

3.1.5. Extreme Values3 min

3.1.6. Extreme Values6 min

3.2.1. Lagrange Multipliers5 min

3.2.2. Lagrange Multipliers3 min

3.2.3. Practice

3.2.4. Practice

3.3.1. Practice quiz: Critical points, extrema, and Lagrange multipliers15 Qns

4. Multiple Integration and Applications

1.5hr

4.1.1. Double Integration (rectangular)7 min

4.1.2. Example: Changing the order of integration5 min

4.1.3. Example: Double integration4 min

4.1.4. Example: Double integration3 min

4.1.5. Double Integration (rectangular)2 min

4.1.6. Example: Volume under a surface5 min

4.2.1. Double Integration (polar)2 min

4.2.2. Example: Double integration (polar)4 min

4.3.1. Triple Integration (rectangular)2 min

4.3.2. Example: Triple integration (rectangular)2 min

4.3.3. Example: Triple integration (rectangular)3 min

4.4.1. Cylindrical coordinates3 min

4.4.2. Triple Integration (cylindrical)56 sec

4.4.3. Example: Cylindrical coordinates9 min

4.4.4. Example: Triple integration (cylindrical)2 min

4.4.5. Example: Triple integration (cylindrical)3 min

4.5.1. Spherical coordinates6 min

4.5.2. Triple Integration (spherical)41 sec

4.5.3. Example: Spherical coordinates5 min

4.5.4. Triple integration (spherical)3 min

4.5.5. Triple integration (spherical)3 min

4.6.1. Improper Integrals3 min

4.6.2. Example: Improper integrals2 min

4.6.3. Example: Improper integrals2 min

4.7.1. Moments and centre of mass3 min

4.7.2. Example: Centroid7 min

4.7.3. Moment of inertia46 sec

4.7.4. Example: Moment of inertia2 min

4.8.1. Practice quiz: Multiple integrals30 Qns

4.8.2. Practice quiz: Centroid, centre of mass, moment of inertia8 Qns

6. Formula Sheet

6.1.1. Formula Sheet

7. Mock Exam

7.1.1. Mock exam20 Qns

MATH 277 Grade Boosters

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