MATH 1004

Carleton University

Course Overview

Lessons & Practice

I. Welcome

1. Functions/Pre-Calculus (Review)

4hr

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. Practice44 sec

1.1.7. Cheatsheet

1.2.1. Domain2 min

1.2.2. Range2 min

1.2.3. Example2 min

1.2.4. Practice 40 sec

1.2.5. Practice 3 min

1.3.1. Operations with Functions3 min

1.3.2. Example2 min

1.3.3. Practice2 min

1.3.4. Practice1 min

1.4.1. Even and Odd Functions3 min

1.4.2. Example2 min

1.5.1. Transformation of Graphs2 min

1.5.2. Example1 min

1.5.3. Practice2 min

1.6.1. Basic of Polynomials4 min

1.6.2. Example2 min

1.6.3. Practice3 min

1.6.4. Polynomial Graphs & Characteristics4 min

1.6.5. Example2 min

1.6.6. Practice2 min

1.7.1. Factoring 5 min

1.7.2. Factoring a Difference & Sum of Cubes3 min

1.7.3. Example2 min

1.7.4. Practice46 sec

1.7.5. Practice2 min

1.7.6. Practice2 min

1.8.1. Dividing Polynomials - Long Division6 min

1.8.2. Example3 min

1.8.3. Dividing Polynomials - Synthetic Division8 min

1.8.4. Example2 min

1.8.5. Practice2 min

1.8.6. Practice3 min

1.9.1. Rational Functions4 min

1.9.2. Solving Rational Equations3 min

1.9.3. Example5 min

1.9.4. Example3 min

1.9.5. Practice6 min

1.9.6. Practice2 min

1.10.1. Radical Functions59 sec

1.10.2. Solving Radical Equations5 min

1.10.3. Example5 min

1.10.4. Practice8 min

1.11.1. Piecewise Functions4 min

1.11.2. Example5 min

1.11.3. Practice3 min

1.12.1. Absolute Value Function1 min

1.12.2. Example3 min

1.13.1. Inverse Functions3 min

1.13.2. Example3 min

1.13.3. Practice2 min

1.14.1. Exponential Functions3 min

1.14.2. Example1 min

1.14.3. Example2 min

1.15.1. Logarithmic Functions4 min

1.15.2. Example3 min

1.15.3. Example:3 min

1.15.4. Practice2 min

1.16.1. Trigonometric Functions6 min

1.16.2. Example4 min

1.16.3. Trig Identities2 min

1.16.4. Practice3 min

1.16.5. Practice4 min

1.17.1. Inverse Trigonometric Functions4 min

1.17.2. Example3 min

1.17.3. Practice2 min

1.17.4. Practice2 min

2. Limits

1.4hr

2.1.1. Limit Basics2 min

2.1.2. Example1 min

2.2.1. One-Sided Limits2 min

2.2.2. Example: One-Sided Limit2 min

2.2.3. Practice: One-Sided Limits3 min

2.3.1. Continuity2 min

2.3.2. Example2 min

2.3.3. Practice4 min

2.4.1. Limit Laws 2 min

2.4.2. Practice1 min

2.5.1. The Fundamental Trig Limit2 min

2.5.2. Example3 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 Intermediate Value Theorem2 min

2.10.2. Example2 min

2.10.3. Practice2 min

2.11.1. Limits at Infinity3 min

2.11.2. Example60 sec

2.11.3. Example3 min

2.11.4. Example4 min

2.11.5. Practice 3 min

2.11.6. Practice3 min

2.12.1. Infinite Limits2 min

2.12.2. Example1 min

2.12.3. Example3 min

2.13.1. The Squeeze Theorem2 min

2.13.2. Example2 min

2.13.3. Practice2 min

3. Derivatives

1.7hr

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

3.3.1. The Power Rule1 min

3.3.2. Example2 min

3.3.3. Practice51 sec

3.4.1. Differentiation Laws51 sec

3.5.1. Normal Lines1 min

3.5.2. Example3 min

3.5.3. Practice

3.5.4. Practice1 min

3.6.1. Tangent Lines1 min

3.6.2. Example3 min

3.6.3. Practice2 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. Implicit Differentiation2 min

3.11.2. Example3 min

3.11.3. Practice3 min

3.11.4. Example3 min

3.12.1. Derivatives of Inverse Functions52 sec

3.12.2. Example2 min

3.12.3. Practice3 min

3.13.1. Inverse Trig Derivatives1 min

3.13.2. Example1 min

3.13.3. Practice3 min

3.14.1. Related Rates1 min

3.14.2. Example5 min

3.14.3. Example4 min

3.14.4. Practice2 min

3.14.5. Practice4 min

3.14.6. Practice4 min

4. Exponentials and Logarithms

22min

4.1.1. Derivatives of Exponential Functions1 min

4.1.2. Example52 sec

4.1.3. Example3 min

4.1.4. Practice1 min

4.2.1. Derivatives of Logarithmic Functions1 min

4.2.2. Example56 sec

4.2.3. Example2 min

4.2.4. Practice2 min

4.2.5. Practice: Log and Ln2 min

4.3.1. Logarithmic Differentiation2 min

4.3.2. Example2 min

4.3.3. Practice3 min

5. Applications of Differentiation

1.4hr

5.1.1. Intervals of Increase and Decrease1 min

5.1.2. Example2 min

5.1.3. Practice3 min

5.2.1. Critical Points and Extrema2 min

5.2.3. Practice3 min

5.3.1. 1st and 2nd Derivative Tests3 min

5.3.2. Example7 min

5.3.4. Practice3 min

5.4.1. Maximum and Minimum on Closed Intervals2 min

5.4.2. Example4 min

5.4.3. Practice3 min

5.4.4. Practice3 min

5.5.1. Concavity and Inflection Points56 sec

5.5.2. Example6 min

5.5.3. Practice6 min

5.6.1. Curve Sketching2 min

5.6.2. Example7 min

5.6.3. Practice9 min

5.7.1. Optimization1 min

5.7.2. Example4 min

5.7.3. Example4 min

5.7.4. Practice6 min

5.7.5. Practice4 min

6. Integration

2hr

6.1.1. Antiderivatives (Indefinite Integral)3 min

6.1.2. Example2 min

6.1.3. Practice1 min

6.1.4. Practice1 min

6.1.5. Practice1 min

6.2.1. Antiderivatives (Indefinite Integral) of Trig Functions4 min

6.2.2. Example1 min

6.2.3. Practice1 min

6.2.4. Practice1 min

6.3.1. Antiderivatives (Indefinite Integrals) of Inverse Trig Functions2 min

6.3.2. Example1 min

6.3.3. Practice1 min

6.4.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

6.4.2. Example42 sec

6.4.3. Practice1 min

6.4.4. Practice2 min

6.5.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

6.5.2. Example2 min

6.5.3. Practice1 min

6.6.1. Initial Conditions2 min

6.6.2. Example2 min

6.6.3. Practice5 min

6.7.1. Finite Sums & Summation Notation3 min

6.7.2. Example5 min

6.7.3. Practice4 min

6.7.4. Practice4 min

6.8.1. Approximating Areas & Riemann Sums 3 min

6.8.2. Example4 min

6.8.3. Practice3 min

6.9.1. The Definite Integrals & Area Under a Curve2 min

6.9.2. Example7 min

6.9.3. Practice2 min

6.9.4. Practice12 min

6.10.1. Properties of the Definite Integral2 min

6.10.2. Practice2 min

6.10.3. Practice2 min

6.11.1. Fundamental Theorem of Calculus - Part I2 min

6.11.2. Example1 min

6.11.3. Example48 sec

6.11.4. Practice1 min

6.11.5. Practice2 min

6.12.1. Fundamental Theorem of Calculus - Part 21 min

6.12.2. Example2 min

6.12.3. Example

6.12.4. Practice 4 min

6.12.5. Practice3 min

6.12.6. Practice1 min

6.13.1. Computing Definite Integrals Geometrically44 sec

6.13.2. Example1 min

6.13.3. Practice1 min

7. Integration Techniques

1.4hr

7.1.1. Integration by Substitution2 min

7.1.2. Example4 min

7.1.3. Example3 min

7.1.4. Example (w/ Back-Substitution)4 min

7.1.5. Practice

7.1.6. Practice

7.1.7. Practice

7.1.8. Practice (w/ Back-Substitution)

7.2.1. New Theory

7.3.1. Integration by Parts3 min

7.3.2. Example5 min

7.3.3. Example3 min

7.3.4. Example6 min

7.3.5. Practice

7.3.6. Practice

7.4.1. Partial Fractions Decomposition4 min

7.4.2. Example: Long Division with Partial Fractions8 min

7.4.3. Example: Rationalizing Substiution5 min

7.4.4. Example: Repeated factors

7.4.5. Practice Question: Partial Fraction

7.4.6. Practice Question: Partial Fraction

7.5.1. Trigonometric Integrals5 min

7.5.2. Example3 min

7.5.3. Example: Trigonometric Integrals (Case 1-3)3 min

7.5.4. Example4 min

7.5.5. Example1 min

7.5.6. Example2 min

7.5.7. Practice

7.5.8. Practice

7.5.9. Practice

7.5.10. Practice

7.6.1. Trigonometric Substitution3 min

7.6.2. Example7 min

7.6.3. Practice

7.6.4. Practice

7.7.1. The Midpoint Rule1 min

7.7.2. Example: The Midpoint Rule2 min

7.8.1. The Trapezoid Rule 1 min

7.8.2. Example2 min

7.9.1. Simpson's Rule1 min

7.9.2. Example2 min

7.10.1. Error Bounds for Approximations2 min

8. Applications of Integration

25min

8.I. Chapter Intro23 sec

8.1.1. Area between curves1 min

8.1.2. Example5 min

8.1.3. Example5 min

8.1.4. Practice

8.1.5. Practice

8.2.1. Volumes of Revolution by Cross Sections (Washers)3 min

8.2.2. Example4 min

8.2.3. Example3 min

8.2.4. Practice

8.2.5. Practice

8.3.1. Volumes of Revolution by Cylindrical Shells2 min

8.3.2. Practice

8.3.3. Practice

8.3.4. Practice

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Welcome to Calc 1!
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