MATH 180

UBC

Course Overview

Grade Boosters

Lessons & Practice

I. Welcome

1. Functions

3hr

1.1.1. Functions7 min

1.1.2. Domain and Range of a Function5 min

1.1.3. Example4 min

1.1.4. Practice (Level 1)56 sec

1.1.5. Practice (Level 2)44 sec

1.1.6. Practice (Level 3)2 min

1.2.1. Linear Equations4 min

1.2.2. Practice Level 113 min

1.2.3. Practice Level 27 min

1.2.4. Parallel & Perpendicular Lines7 min

1.2.5. Practice Level 35 min

1.3.1. Activity: Exploring Quadratic Relations

1.3.2. Quadratic Functions3 min

1.3.3. Example7 min

1.3.4. Practice Level 15 min

1.3.5. Practice Level 25 min

1.3.6. Practice Level 2

1.3.7. Practice Level 37 min

1.4.1. Rational Functions4 min

1.4.2. Solving Rational Equations3 min

1.4.3. Example5 min

1.4.4. Example3 min

1.4.5. Practice6 min

1.4.6. Practice2 min

1.5.1. Radical Functions59 sec

1.5.2. Solving Radical Equations5 min

1.5.3. Example5 min

1.5.4. Practice8 min

1.6.1. Piecewise Functions4 min

1.6.2. Example5 min

1.6.3. Practice3 min

1.7.1. Absolute Value Function1 min

1.7.2. Example3 min

1.8.1. Exponential Functions3 min

1.8.2. Example1 min

1.8.3. Example2 min

1.9.1. Logarithmic Functions4 min

1.9.2. Example3 min

1.9.3. Example:3 min

1.9.4. Practice2 min

1.10.1. Trigonometric Functions6 min

1.10.2. Example4 min

1.10.3. Trig Identities2 min

1.10.4. Practice3 min

1.10.5. Practice4 min

1.11.1. Inverse Trigonometric Functions4 min

1.11.2. Example3 min

1.11.3. Practice2 min

1.11.4. Practice2 min

2. Limits & Continuity

1.9hr

2.1.1. Limit Basics2 min

2.1.2. Example1 min

2.2.1. Limit Laws 2 min

2.2.2. Practice1 min

2.3.1. One-Sided Limits2 min

2.3.2. Example: One-Sided Limit2 min

2.3.3. Practice: One-Sided Limits3 min

2.4.1. Infinite Limits2 min

2.4.2. Example1 min

2.4.3. Example3 min

2.5.1. Limits at Infinity3 min

2.5.2. Example60 sec

2.5.3. Example3 min

2.5.4. Example4 min

2.5.5. Practice 3 min

2.5.6. Practice3 min

2.6.1. Indeterminate Forms50 sec

2.7.1. Computing Limits by Factoring1 min

2.7.2. Example1 min

2.7.3. Practice2 min

2.8.1. Computing Limits by Multiplying by the Conjugate3 min

2.8.2. Example3 min

2.8.3. Practice3 min

2.9.1. Computing Limits by Getting a Common Denominator1 min

2.9.2. Example2 min

2.9.3. Practice4 min

2.10.1. The Fundamental Trig Limit2 min

2.10.2. Example3 min

2.11.1. The Squeeze Theorem2 min

2.11.2. Example2 min

2.11.3. Practice2 min

2.12.1. Continuity2 min

2.12.2. Example2 min

2.12.3. Practice4 min

2.13.1. The Intermediate Value Theorem2 min

2.13.2. Example2 min

2.13.3. Practice2 min

2.14.1. The Epsilon Delta Definition of a Limit

2.14.2. Example3 min

2.14.3. Practice

3. Derivative Rules & Derivative of Functions

2.8hr

3.1.1. Derivatives as a Rate of Change2 min

3.1.2. Average Rate of Change46 sec

3.1.3. Example2 min

3.1.4. Practice1 min

3.2.1. The Limit Definition of a Derivative2 min

3.2.2. Example3 min

3.2.3. Practice5 min

3.2.4. When is Function Not Differentiable?

3.3.1. Differentiation Laws51 sec

3.4.1. The Power Rule1 min

3.4.2. Example2 min

3.4.3. Practice51 sec

3.5.1. Tangent Lines1 min

3.5.2. Example3 min

3.5.3. Practice2 min

3.6.1. Normal Lines1 min

3.6.2. Example3 min

3.6.3. Practice1 min

3.7.1. The Product Rule49 sec

3.7.2. Example2 min

3.7.3. Example2 min

3.7.4. Practice2 min

3.8.1. The Quotient Rule1 min

3.8.2. Example2 min

3.8.3. Practice4 min

3.9.1. The Chain Rule1 min

3.9.2. Example2 min

3.9.3. Practice3 min

3.10.1. Derivatives of Trigonometric Functions1 min

3.10.2. Example39 sec

3.10.3. Example3 min

3.10.4. Example1 min

3.10.5. Practice3 min

3.10.6. Practice2 min

3.11.1. Derivatives of Exponential Functions1 min

3.11.2. Example52 sec

3.11.3. Example3 min

3.11.4. Practice1 min

3.12.1. Higher Order Derivatives2 min

3.12.2. Example3 min

3.12.3. Practice2 min

3.12.4. Practice2 min

3.13.1. Implicit Differentiation2 min

3.13.2. Example3 min

3.13.3. Example3 min

3.13.4. Practice3 min

3.14.1. Derivatives of Inverse Functions52 sec

3.14.2. Example2 min

3.14.3. Practice3 min

3.15.1. Derivatives of Logarithmic Functions1 min

3.15.2. Example56 sec

3.15.3. Example2 min

3.15.4. Practice2 min

3.15.5. Practice: Log and Ln2 min

3.16.1. Inverse Trig Derivatives1 min

3.16.2. Example1 min

3.16.3. Practice3 min

3.17.1. Logarithmic Differentiation2 min

3.17.2. Example2 min

3.17.3. Practice3 min

3.18.1. Hyperbolic Functions and their Derivatives2 min

3.18.2. Example51 sec

3.18.3. Practice59 sec

3.19.1. Inverse Hyperbolic Functions and their Derivatives37 sec

3.19.2. Practice

4. Applications of Differentiation

4hr

4.1.1. Related Rates1 min

4.1.2. Example5 min

4.1.3. Example4 min

4.1.4. Practice2 min

4.1.5. Practice4 min

4.1.6. Practice4 min

4.2.1. Differentials2 min

4.2.2. Example3 min

4.2.3. Practice2 min

4.3.1. Linearization (Linear Approximation)59 sec

4.3.2. Example3 min

4.3.3. Practice3 min

4.3.4. Practice3 min

4.4.1. Newton's Method1 min

4.4.3. Example4 min

4.4.4. Practice

4.4.5. Practice2 min

4.5.1. L’Hopital’s Rule2 min

4.5.2. Example2 min

4.5.3. Practice5 min

4.6.1. Solving General Indeterminate Forms2 min

4.6.2. Example2 min

4.6.3. Practice5 min

4.6.4. Practice2 min

4.7.1. Extreme Value Theorem1 min

4.8.1. Rolle's Theorem1 min

4.8.2. Example2 min

4.8.3. Practice1 min

4.9.1. Fermat's Theorem47 sec

4.10.1. The Mean Value Theorem1 min

4.10.2. Example2 min

4.10.3. Practice2 min

4.11.1. Intervals of Increase and Decrease1 min

4.11.2. Example2 min

4.11.3. Practice3 min

4.12.1. Critical Points and Extrema2 min

4.12.2. Example

4.12.3. Practice3 min

4.13.1. 1st and 2nd Derivative Tests3 min

4.13.2. Example7 min

4.13.3. Example

4.13.4. Practice3 min

4.14.1. Maximum and Minimum on Closed Intervals2 min

4.14.2. Example4 min

4.14.3. Practice3 min

4.14.4. Practice3 min

4.15.1. Concavity and Inflection Points56 sec

4.15.2. Example6 min

4.15.3. Practice6 min

4.16.1. Curve Sketching2 min

4.16.2. Example7 min

4.16.3. Practice9 min

4.16.4. Practice

4.17.1. Exponential Growth and Decay3 min

4.17.2. Example4 min

4.17.3. Example5 min

4.17.4. Practice5 min

4.18.1. Newton’s Law of Cooling1 min

4.18.2. Example5 min

4.18.3. Practice2 min

4.19.1. Related Rates

4.19.2. Related Rates5 min

4.19.3. Related Rates5 min

4.19.4. Linear Approximation4 min

4.19.5. Linear Approximation

4.19.6. Taylor Series from Definition7 min

4.19.7. Taylor Polynomials

4.19.8. Maclaurin Polynomial

4.19.9. Newton's Method2 min

4.19.10. Newton's Method

4.19.11. L'Hopital's Rule

4.19.12. L'Hopital's Rule

4.19.13. L'Hopital's Rule

4.19.14. Limits

4.19.15. L'Hopital's Rule

4.19.16. L'Hopital's Rule

4.19.17. Limits

4.19.18. Limits

4.19.19. Extreme Value Theorem

4.19.20. Rolle's Theorem1 min

4.19.21. Rolle's Theorem6 min

4.19.23. MVT2 min

4.19.24. MVT3 min

4.19.26. Intervals of Increase and Decrease

4.19.27. Intervals of Increase and Decrease3 min

4.19.28. Critical Points6 min

4.19.29. Critical Points1 min

4.19.30. Extrema5 min

4.19.31. Extrema6 min

4.19.32. Second Derivative Test10 min

4.19.33. Curve Sketching

4.19.34. Curve Sketching12 min

4.19.35. Curve Sketching

4.19.36. Optimization

4.19.37. Optimization

4.19.38. Optimization

5. Geometric Series, Taylor Polynomials, & Optimization

1.5hr

6. Differential Equations & Applications

1.5hr

6.1.1. Differential Equations8 min

6.1.2. Direction Fields/Slope Fields5 min

6.1.3. Practice Question: DE Solution Graphs3 min

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

6.1.5. Practice

6.2.1. Separable First Order Differential Equations3 min

6.2.2. Practice (separable DE)2 min

6.2.3. Practice (IVP)3 min

6.2.4. Practice (IVP)3 min

6.2.5. Practice (IVP*)5 min

6.2.6. Practice (separable DE)1 min

6.3.1. Linear First Order Differential Equations7 min

6.3.2. Practice (integrating factor)1 min

6.3.3. Practice (linear DE)3 min

6.3.4. Practice (IVP)3 min

6.3.5. Practice (IVP)4 min

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

6.4.2. Euler's Method (for approximating solution8 min

6.4.3. Practice: Euler's Method2 min

6.4.4. Practice

6.5.1. Common DE Applications (Word Problems)

6.5.2. Practice (population)3 min

6.5.3. Practice (population)4 min

6.5.4. Practice (cooling & heating)3 min

6.5.5. Practice (mixing tank)6 min

6.5.6. Practice (mixing tank)8 min

7. Functions of Several Variables

2hr

7.1.1. Functions of Several Variables5 min

7.1.2. Practice3 min

7.2.1. Functions of 2 & 3 Variables and Contour Curves5 min

7.2.2. Contour Diagram3 min

7.2.3. Practice Question1 min

7.2.4. Practice: Match the map with the equation9 min

7.3.1. Partial derivatives6 min

7.3.2. Example: Partial derivatives3 min

7.3.3. Practice: First Partial derivatives2 min

7.3.4. Practice: Second Partial Derivatives3 min

7.4.1. Tangent Plane5 min

7.4.2. Example: Tangent Planes2 min

7.4.3. Example: Tangent Planes3 min

7.4.4. Practice: Linear Approximation2 min

7.4.5. Practice: Tangent Plane2 min

7.5.1. Chain Rule7 min

7.5.2. Example: Chain Rule (1)2 min

7.5.3. Example: Chain Rule (2)1 min

7.5.4. Practice: Chain Rule2 min

7.5.5. Practice: Chain Rule2 min

7.5.6. Practice: Chain Rule*3 min

7.5.7. Implicit Differentiation2 min

7.6.1. Differentials4 min

7.6.2. Practice: Differentials

7.6.3. Practice: Differentials

7.7.1. Maximums, Minimums, and Critical Points5 min

7.7.2. Example5 min

7.7.3. Example5 min

7.7.4. Practice4 min

7.7.5. Practice3 min

7.8.1. Local Max & Min4 min

7.8.2. Absolute Max & Min5 min

7.8.3. Lagrange Multipliers3 min

7.8.4. Practice: Lagrange Multipliers

7.8.5. Practice: Lagrange Multipliers

7.9.1. Lagrange Multipliers3 min

7.9.2. Example3 min

7.9.4. Practice3 min

7.9.5. Practice4 min

Mock Exams

ME.1. Mock Exam (Similar to 2016 Final Exam)37 Qns

ME.2. Test 1 - Mock Assessment32 Qns

ME.3. Test 2 - Mock Assessment31 Qns

ME.4. Final Exam - Mock Assessment45 Qns

Test 2 Overview

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