MATH 157

SFU

Course Overview

Lessons & Practice

I. Welcome

1. Review

9hr

1.1.1. Interval Notation 4 min

1.1.2. Set Notation3 min

1.1.3. Example4 min

1.1.4. Practice2 min

1.1.5. Practice52 sec

1.1.6. Cheatsheet

1.2.1. Powers & Exponents9 min

1.2.2. Practice Level 13 min

1.2.3. Practice Level 12 min

1.2.4. Practice Level 23 min

1.2.5. Practice Level 33 min

1.2.6. Practice Level 3 (Financial Application)8 min

1.3.1. Exponent Rules4 min

1.4.1. Exponent Rules for Fractions & Products5 min

1.4.2. Example3 min

1.4.3. Practice Level 12 min

1.4.4. Practice Level 12 min

1.4.5. Practice Level 23 min

1.4.6. Practice Level 34 min

1.5.1. Exponent Product Rule for Multiplying Powers3 min

1.5.2. Example2 min

1.5.3. Practice Level 13 min

1.5.4. Practice Level 25 min

1.6.1. Exponent Quotient Rule for Dividing Powers3 min

1.6.2. Example2 min

1.6.3. Practice Level 14 min

1.6.4. Practice Level 24 min

1.7.1. Exponent Power of a Power Rule3 min

1.7.2. Example56 sec

1.7.3. Practice Level 14 min

1.7.4. Practice Level 24 min

1.7.5. Example (⭐Important!)4 min

1.7.6. Practice Level 34 min

1.8.1. Practice Level 15 min

1.8.2. Practice Level 23 min

1.8.3. Practice Level 37 min

1.9.1. Investigating Integer Exponents6 min

1.9.2. Integer Exponents1 min

1.9.3. Practice1 min

1.9.4. Practice4 min

1.9.5. Practice3 min

1.10.1. Factored Form of a Quadratic Equation9 min

1.10.2. Example8 min

1.10.3. Practice Level 14 min

1.10.4. Practice Level 27 min

1.10.5. Practice Level 35 min

1.10.6. Summary - Factored Form of a Quadratic Equation

1.11.1. Example7 min

1.11.2. Practice Level 16 min

1.11.3. Example5 min

1.11.4. Practice Level 211 min

1.11.5. Practice Level 34 min

1.11.6. Practice Level 3 🔥3 min

1.12.1. Solving Inequalities2 min

1.12.2. Example (Single Step Inequalities)5 min

1.12.3. Practice Level 12 min

1.12.4. Practice Level 13 min

1.12.5. Example (Multi-Step Inequalities)3 min

1.12.6. Practice Level 22 min

1.12.7. Practice Level 33 min

1.12.8. Practice Level 33 min

1.13.1. Solving Linear Inequalities in Two Variables5 min

1.13.2. Example5 min

1.13.3. Practice Level 13 min

1.13.4. Practice Level 36 min

1.13.5. Solving Quadratic Inequalities in Two Variables5 min

1.13.6. Example3 min

1.13.7. Practice Level 13 min

1.13.8. Practice Level 23 min

1.14.1. Solving Quadratic Inequalities in One Variable7 min

1.14.2. Example4 min

1.14.3. Practice Level 13 min

1.14.4. Practice Level 23 min

1.14.5. Practice Level 3

1.15.1. Piecewise Functions4 min

1.15.2. Example5 min

1.15.3. Practice Level 13 min

1.15.4. Practice Level 24 min

1.15.5. Practice Level 32 min

1.16.1. Absolute Value4 min

1.16.2. Example2 min

1.16.3. Practice Level 12 min

1.16.4. Practice Level 23 min

1.16.5. Practice Level 33 min

1.17.1. Absolute Value Functions6 min

1.17.2. Example5 min

1.17.3. Practice Level 144 sec

1.17.4. Practice Level 23 min

1.17.5. Practice Level 35 min

1.18.1. Solving Absolute Value Equations5 min

1.18.2. Practice Level 12 min

1.18.3. Example4 min

1.18.4. Practice Level 24 min

1.18.5. Practice Level 33 min

1.19.1. Pythagorean Theorem5 min

1.19.2. Example5 min

1.19.3. Practice6 min

1.20.1. Midpoint of a Line Segment2 min

1.20.2. Example2 min

1.20.3. Practice Level 12 min

1.20.4. Practice Level 24 min

1.20.5. Practice Level 37 min

1.21.1. Length of a Line Segment2 min

1.21.2. Example3 min

1.21.3. Practice Level 12 min

1.21.4. Practice Level 23 min

1.21.5. Practice Level 39 min

1.22.1. Equation of a Circle around the Centre (Origin)2 min

1.22.2. Example3 min

1.22.3. Practice Level 13 min

1.22.4. Practice Level 23 min

1.23.1. Primary Trig Ratios --

\ \sin

\cos

\tan

5 min

1.23.2. Practice Level 1

1.23.3. Example2 min

1.23.4. Practice Level 22 min

1.23.5. Example3 min

1.23.6. Practice Level 22 min

1.23.7. Practice Level 22 min

1.23.8. Practice Level 32 min

1.24.1. Right Angle Triangle Problems1 min

1.24.2. Example6 min

1.24.3. Practice Level 36 min

1.24.4. Practice Level 32 min

1.24.5. Practice Level 33 min

1.24.6. Practice Level 33 min

1.25.1. Reciprocal Trig Ratios --

\ \csc

\sec

\cot

5 min

1.25.2. Example2 min

1.25.3. Practice Level 1

1.25.4. Practice Level 22 min

1.25.5. Practice Level 33 min

1.26.1. Special Angles & Special Triangles (Degrees)5 min

1.26.2. Example5 min

1.26.3. Practice Level 13 min

1.26.4. Practice Level 23 min

1.27.1. Trig Ratios for Angles Between 0° and 360°6 min

1.27.2. Example2 min

1.27.3. Practice Level 12 min

1.27.4. Practice Level 23 min

1.27.5. Practice Level 2

1.28.1. Solving Simple Trigonometric Equations5 min

1.28.2. Example4 min

1.28.3. Practice Level 12 min

1.28.4. Practice Level 23 min

1.28.5. Example3 min

1.28.6. Practice Level 32 min

2. Functions

3hr

2.1.1. Domain2 min

2.1.2. Range2 min

2.1.3. Example2 min

2.1.4. Practice 40 sec

2.1.5. Practice 3 min

2.2.1. Operations with Functions3 min

2.2.2. Example2 min

2.2.3. Practice2 min

2.2.4. Practice1 min

2.3.1. Even and Odd Functions3 min

2.3.2. Example2 min

2.4.1. Transformation of Graphs2 min

2.4.2. Example1 min

2.4.3. Practice2 min

2.5.1. Basic of Polynomials4 min

2.5.2. Example2 min

2.5.3. Practice3 min

2.5.4. Polynomial Graphs & Characteristics4 min

2.5.5. Example2 min

2.5.6. Practice2 min

2.6.1. Factoring 5 min

2.6.2. Factoring a Difference & Sum of Cubes3 min

2.6.3. Example2 min

2.6.4. Practice46 sec

2.6.5. Practice2 min

2.6.6. Practice2 min

2.7.1. Dividing Polynomials - Long Division6 min

2.7.2. Example3 min

2.7.3. Dividing Polynomials - Synthetic Division8 min

2.7.4. Example2 min

2.7.5. Practice2 min

2.7.6. Practice3 min

2.8.1. Rational Functions4 min

2.8.2. Solving Rational Equations3 min

2.9.1. Radical Functions59 sec

2.9.2. Solving Radical Equations5 min

2.9.3. Example5 min

2.9.4. Practice8 min

2.10.1. Piecewise Functions4 min

2.10.2. Example5 min

2.10.3. Practice3 min

2.11.1. Absolute Value Function1 min

2.11.2. Example3 min

2.12.1. Inverse Functions3 min

2.12.2. Example3 min

2.12.3. Practice2 min

2.13.1. Exponential Functions3 min

2.13.2. Example1 min

2.13.3. Example2 min

2.14.1. Logarithmic Functions4 min

2.14.2. Example3 min

2.14.3. Example:3 min

2.14.4. Practice2 min

2.15.1. Trigonometric Functions6 min

2.15.2. Example4 min

2.15.3. Trig Identities2 min

2.15.4. Practice3 min

2.15.5. Practice4 min

2.16.1. Inverse Trigonometric Functions4 min

2.16.2. Example3 min

2.16.3. Practice2 min

2.16.4. Practice2 min

3. Limits and Continuity

1.7hr

3.1.1. Limit Basics2 min

3.1.2. Example1 min

3.2.1. Limit Laws 2 min

3.2.2. Practice1 min

3.3.1. One-Sided Limits2 min

3.3.2. Example: One-Sided Limit2 min

3.3.3. Practice: One-Sided Limits3 min

3.4.1. Infinite Limits2 min

3.4.2. Example1 min

3.4.3. Example3 min

3.5.1. Limits at Infinity3 min

3.5.2. Example60 sec

3.5.3. Example3 min

3.5.4. Example4 min

3.5.5. Practice 3 min

3.5.6. Practice3 min

3.6.1. Indeterminate Forms50 sec

3.7.1. Computing Limits by Factoring1 min

3.7.2. Example1 min

3.7.3. Practice2 min

3.8.1. Computing Limits by Multiplying by the Conjugate3 min

3.8.2. Example3 min

3.8.3. Practice3 min

3.9.1. Computing Limits by Getting a Common Denominator1 min

3.9.2. Example2 min

3.9.3. Practice4 min

3.10.1. The Fundamental Trig Limit2 min

3.10.2. Example3 min

3.11.1. The Squeeze Theorem2 min

3.11.2. Example2 min

3.11.3. Practice2 min

3.12.1. Continuity2 min

3.12.2. Example2 min

3.12.3. Practice4 min

3.13.1. The Intermediate Value Theorem2 min

3.13.2. Example2 min

3.13.3. Practice2 min

3.14.1. One-sided Limits

3.14.2. Limits

3.14.3. Special Limits4 min

3.14.10. Limits: Indeterminate forms

3.14.15. Fundamental Trig Limit5 min

3.14.16. Fundamental Trig Limit3 min

3.14.17. Continuity

4. The Derivative & Differentiation Techniques

2.5hr

4.1.1. Derivatives as a Rate of Change2 min

4.1.2. Example2 min

4.1.3. Practice1 min

4.2.1. Differentiation Laws51 sec

4.3.1. The Power Rule1 min

4.3.2. Example2 min

4.3.3. Practice51 sec

4.4.1. Tangent Lines1 min

4.4.2. Example3 min

4.4.3. Practice2 min

4.5.1. Normal Lines1 min

4.5.2. Example3 min

4.5.3. Practice1 min

4.6.1. The Product Rule49 sec

4.6.2. Example2 min

4.6.3. Example2 min

4.6.4. Practice2 min

4.7.1. The Quotient Rule1 min

4.7.2. Example2 min

4.7.3. Practice4 min

4.8.1. The Chain Rule1 min

4.8.2. Example2 min

4.8.3. Practice3 min

4.9.1. Derivatives of Trigonometric Functions1 min

4.10.1. Derivatives of Exponential Functions1 min

4.10.2. Example52 sec

4.10.3. Example3 min

4.10.4. Practice1 min

4.11.1. Derivatives of Logarithmic Functions1 min

4.11.2. Example56 sec

4.11.3. Example2 min

4.11.4. Practice2 min

4.11.5. Practice: Log and Ln2 min

4.12.1. Higher Order Derivatives2 min

4.12.2. Example3 min

4.12.3. Practice2 min

4.12.4. Practice2 min

4.13.1. Implicit Differentiation2 min

4.13.2. Example3 min

4.13.3. Example3 min

4.13.4. Practice3 min

4.14.1. Logarithmic Differentiation2 min

4.14.2. Example2 min

4.14.3. Practice3 min

4.15.1. Derivatives of Inverse Functions52 sec

4.15.2. Example2 min

4.15.3. Practice3 min

4.16.1. Inverse Trig Derivatives1 min

4.16.2. Example1 min

4.16.3. Practice3 min

5. Applications of Differentiation

4hr

5.1.1. Elasticity of Demand2 min

5.1.2. Example3 min

5.1.3. Practice: Elasticity of Demand4 min

5.2.1. Related Rates1 min

5.3.1. Linearization (Linear Approximation)59 sec

5.3.2. Example3 min

5.3.3. Practice3 min

5.3.4. Practice3 min

5.4.1. Differentials2 min

5.4.2. Example3 min

5.4.3. Practice2 min

5.5.1. Newton's Method1 min

5.6.1. L’Hopital’s Rule2 min

5.6.2. Example2 min

5.6.3. Practice5 min

5.7.1. Critical Points and Extrema2 min

5.7.2. Example

5.7.3. Practice3 min

5.8.1. Extreme Value Theorem1 min

5.9.1. The Mean Value Theorem1 min

5.9.2. Example2 min

5.9.3. Practice2 min

5.10.1. Intervals of Increase and Decrease1 min

5.10.2. Example2 min

5.10.3. Practice3 min

5.11.1. Maximum and Minimum on Closed Intervals2 min

5.11.2. Example4 min

5.11.3. Practice3 min

5.11.4. Practice3 min

5.12.1. Concavity and Inflection Points56 sec

5.12.2. Example6 min

5.12.3. Practice6 min

5.13.1. 1st and 2nd Derivative Tests3 min

5.13.2. Example7 min

5.13.3. Example

5.13.4. Practice3 min

5.14.1. Curve Sketching2 min

5.14.2. Example7 min

5.14.3. Practice9 min

5.14.4. Practice

5.15.1. Optimization1 min

5.15.2. Example4 min

5.15.3. Example4 min

5.15.4. Practice6 min

5.15.5. Practice4 min

5.16.1. Related Rates

5.16.2. Related Rates5 min

5.16.3. Related Rates5 min

5.16.4. Linear Approximation4 min

5.16.5. Linear Approximation

5.16.6. Newton's Method2 min

5.16.7. Newton's Method

5.16.8. L'Hopital's Rule

5.16.9. L'Hopital's Rule

5.16.10. L'Hopital's Rule

5.16.11. Limits

5.16.12. L'Hopital's Rule

5.16.13. L'Hopital's Rule

5.16.14. Limits

5.16.15. Limits

5.16.16. Extreme Value Theorem

5.16.17. Rolle's Theorem1 min

5.16.18. Rolle's Theorem6 min

5.16.19. Intervals of Increase and Decrease

5.16.20. Intervals of Increase and Decrease3 min

5.16.21. Critical Points6 min

5.16.22. Critical Points1 min

5.16.23. Extrema5 min

5.16.24. Extrema6 min

5.16.25. Second Derivative Test10 min

5.16.26. Curve Sketching

5.16.27. Curve Sketching12 min

5.16.28. Curve Sketching

5.16.29. Optimization

5.16.30. Optimization

5.16.31. Optimization

5.16.32. Elasticity of Demand

6. Multi-Variable Calculus

54min

6.1.1. Functions of Several Variables5 min

6.1.2. Practice3 min

6.2.1. Partial derivatives6 min

6.2.2. Practice: First Partial derivatives2 min

6.2.3. Practice: Second Partial Derivatives3 min

6.3.1. Chain Rule7 min

6.3.2. Practice: Chain Rule2 min

6.3.3. Practice: Chain Rule2 min

6.3.4. Practice: Chain Rule*3 min

6.3.5. Implicit Differentiation2 min

6.4.1. Gradient and directional derivative7 min

6.4.2. Practice: Gradient and directional derivative

6.5.1. Local Max & Min4 min

6.5.2. Absolute Max & Min5 min

6.5.3. Lagrange Multipliers3 min

6.5.4. Practice: Lagrange Multipliers

6.5.5. Practice: Lagrange Multipliers

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Midterm 2 Overview

Course Notes

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