Video Lectures

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Chapter 1: Algebra Review

Solutions to Practice Problems from Chapter 1

1: Volume of a Box
2: Law of Exponents
3: Domain of a function
4: Domain of a function
5: A quadratic inequality
6: A quadratic inequality
7: A quadratic inequality
8: Domain of a function
9: Domain of a function
10: Absolute value inequality
11: Composition of functions
12: Composition of functions
13: Composition of functions
 14: Composition of functions
15: Composition of functions
16: Composition of functions
17: Composition of functions
18: Equation of a line
19: Equation of a line
20: Equation of a line
21: Equation of a line
22: Equation of a line
23: Equation of a line
24: Equation of a line
25: Equation of a parabola
26: System of quadratic equations


Chapter 2: Rates of Change

Practice Problems from Chapter 2

1: Average velocity
2: Average velocity
3: Average velocity
4: Average velocity
5: Average velocity
6: Average velocity
7: Average rate of change of a function
8: Average rate of change of a function
9: Average rate of change of a function
10: Average rate of change of a function
11: Average rate of change of a function
12: Average rate of change of a function
13: Average rate of change of a function
14: Simplifying a difference quotient
15: Simplifying a difference quotient
16: Simplifying a difference quotient
17: Simplifying a difference quotient
18: Simplifying a difference quotient
 19: Simplifying a difference quotient
20: Instantaneous rate of change
21: Instantaneous rate of change
22: Instantaneous rate of change
23: Instantaneous rate of change
24: Instantaneous rate of change
25: Instantaneous rate of change
26: Instantaneous rate of change
27: Instantaneous rate of change
28: Slope of tangent line
29: Equation of tangent line
30: Tangent line
31: Tangent line
32: Slope of tangent line
33: Tangent line
34: Object falling due to gravity
35: Object falling due to gravity
36: Average and Instantaneous rates of change


Chapter 3: Limits

Practice Problems from Chapter 3

1: Computing a limit
2: Computing a limit
3: Computing a limit
4: Computing a limit
5: Computing a limit
6: Computing a limit
7: Computing a limit
8: Computing a limit
9: Computing a limit
10: Computing a limit
11: Computing a limit
12: Computing a limit
13: Computing a one-sided limit
14: Computing a one-sided limit
15: Computing a one-sided limit
16: Computing a one-sided limit
 17: Computing a one-sided limit
18: Computing a one-sided limit
19: Computing a one-sided limit
20: Limit of average cost
21: Computing a limit at infinity
22: Computing a limit at infinity
23: Computing a limit at infinity
24: Computing a limit at infinity
25: Limit of an average cost
26: Continuity and piecewise defined functions
27: Continuity and piecewise defined functions
28: Continuity and piecewise defined functions
29: Continuity and piecewise defined functions
30: Continuity and piecewise defined functions
31: Continuity
32: Differentiability


Chapter 4: Computing Some Derivatives

Examples 7 through 11 in chapter 4 involve a lot of algebraic manipulation. The point of these video lectures is to cover these examples in more detail than a single 50 minute lecture allows. You may also want to look at pages 69-82 of the Gootman textbook for a more in depth review of algebra.
Chapter 4 example 7
Chapter 4 example 8
Chapter 4 example 9
Chapter 4 example 10
Chapter 4 examples 11
Chapter 4 examples 12
Chapter 4 examples 11

Practice Problems from Chapter 4

1: Simplifying a difference quotient
2: Simplifying a difference quotient
3: Slope of a tangent line
4: Simplifying a difference quotient
5: Simplifying a difference quotient
6: Computing a derivative
 7: Equation of a tangent line
8: Numerical approximation of a derivative
9: Numerical approximation of a derivative
10: Numerical approximation of a derivative
11: Numerical approximation of a derivative


Chapter 5: Formulas for Derivatives

Practice Problems from Chapter 5

1: Power Rule
2: Power Rule
3: Computing a derivative
4: Computing a derivative
5: Computing a derivative
6: Computing a derivative
7: Computing a derivative
8: Differentiability
9: Product Rule
10: Product Rule
11: Product Rule
12: Product Rule
13: Quotient Rule
14: Quotient Rule
15: Power Rule
16: Quotient Rule
17: Quotient Rule
18: Quotient Rule
19: Marginal Cost
20: Horizontal Tangent Line
21: Quotient Rule
22: Quotient Rule
23: Quotient Rule
24: Tangent Line
25: Tangent Line
 26: Tangent Line
27: Tangent Line
28: Tangent Line
29: Tangent Line
30: Product Rule and Tangent Line
31: Tangent Line
32: Tangent Line
33:
34: Chain Rule
35: Chain Rule
36: Chain Rule
37: Chain Rule
38: Chain Rule and definition of derivative
39: Chain Rule
40: Chain Rule
41: Chain Rule
42: Chain Rule and Product Rule
43: Chain Rule
44: Chain Rule and Tangent Line
45: Chain Rule
46: Chain Rule
47: Tangent Line
48: Chain Rule
49: Second Derivative


Supplement: Exponential and logarithmic functions

Practice Problems from Supplement on Exponential and Logarithmic functions

1: Derivative of a logarithmic function
2: Derivative of an exponential function
3: Derivative of an exponential function
4: Equation of a tangent line
 5: Finding continuous growth rate
6: Number of bacteria
7: Tripling time of an investment


Chapter 6: Extreme Values, Mean Value Theorem, Increasing/Decreasing Funtions, Concavity

1: Minimum Value
2: Maximum Value
3: Minimum Value
4: Maximum Value
5: Minimum Value
6: Maximum Value
7: Minimum Value
8: Maximum Value
9: Minimum Value
10: Minimum Value
11: Minimum Value
12: Average and Instantaneous Rate of Change
13: Mean Value Theorem
14: Mean Value Theorem
15: Mean Value Theorem
 16 and 17: Increasing and decreasing functions
18, 21, 22: Increasing and decreasing functions
19 and 20: Increasing and decreasing functions
24, 23, 26: Increasing and decreasing functions
25 and 27: Increasing and decreasing functions
28, 29, 30: Extreme values, increasing and decreasing functions
31 and 32: Extreme values, increasing and decreasing functions
33 and 34: Extreme values, increasing and decreasing functions
35: Concavity
36: Concavity
37: Concavity
38: Concavity
39: Concavity


Chapter 7: Word Problems

Chapter 7 Example 4: The Norman Winow
Chapter 7 Example 5: Area of largest inscribed rectangle
Chapter 7 Example 6: Shortest length of a path
Chapter 7 Examples 15 and 16: Rate of change of depth

Practice Problems on Optimization

1: A field with maximal area
2: Inscribed rectangle with maximal area
3: Maximizing revenue
4: Inscribed rectangle with maximal area
5: Shortest distance
6: Inscribed triangle with minimal area
7: Inscribed rectangle with maximal area
8: Inscribed rectangle with maximal area
9: Area of field with maximal area
10: Shortest distance
11: Shortest distance
12: Minimizing a sum with a constraint
13: Maximizing a product with a constraint
14: Minimizing a sum with a constraint
15: Inscribed rectangle with maximal area
16: Inscribed rectangle with maximal area
17: Shortest distance

Practice Problems on Related Rates

18: Rate of change of distance between two objects
19: Rate of change of depth of water in a tank
20: Rate of change of area of a triangle
21: Rate of change of distance between two objects
22: Rate of change of depth of water in a tank
23: Velocity in horizontal direction
24: Rate of change of distance between two objects
25: Rate of change of height of sand in a sandbox
26: Rate of change of sides of a rectangle with fixed area
27: Rate of change of distance between two objects
28: Rate of change of temperature
29: Rate of change of depth of water in a pool
30: Rate of change of distance between two objects
31: Rate of change of distance between two objects
32: Rate of change of area of an expanding circle
33: Rate of change of area of rectangle
34: Rate of change of area of rectangle


Chapter 8: Idea of Integral

Practice Problems from Chapter 8

Some of the following examples were previously in Chapter 9, but is now appropriate for Chapter 8.

1: Integral of step-wise function
2: Distance travelled by train
3: Computing an integral
4: Computing an integral
5: Computing an integral
6: Computing an integral
7: Computing an integral


Chapter 9: Estimating definite integrals

Practice Problems from Chapter 9

Some of these examples were previously in Chapter 8, but are now appropriate for Chapter 9.

1: Estimating area under curve
2: Estimating area under curve
4: Estimating area under curve
5: Estimating area under curve
6: Estimating area under curve
7: Estimating area under curve
8: Estimating area under curve
9: Estimating area under curve
10: Estimating area under curve
11: Estimating area under curve
12: Comparing different estimates
13: Computing an integral


Chapter 10: Fundamental Theorem of Calculus

Practice Problems from Chapter 10

1: Derivative of an integral
2: Derivative of an integral
3: Derivative of an integral
4: Maximizing an integral
5: Integration via antidifferentiation
6: Integration via antidifferentiation
7: Computing an integral
 8: Computing an integral
9: Computing an integral
10: Integration by substitution
11: Integration by substitution
12: Antidifferentiation
13: Average value
14: Average value