Math 152: Calculus I

Catalog course description: A study of the basic concepts and techniques of calculus for students in all disciplines. Topics include limits, differentiation, integration, and applications.

Syllabus

The syllabus is available here.

Slides

Slides from each lecture (as numbered in the syllabus) are available via the links below.

• Lecture 1 What is Velocity?
• Lecture 2 Limits
• Lecture 3 The Derivative at a Point
• Lecture 4 The Derivative Function
• Lecture 5 Interpreting the Derivative
• Lecture 6 The Second Derivative
• Lecture 7 Limits, Continuity, and Differentiability
• Lecture 8 The Tangent Line Approximation
• Lecture 9 Elementary Derivative Rules
• Lecture 10 Sine and Cosine
• Lecture 11 Product and Quotient Rules
• Lecture 12 Derivatives of Other Trig Functions
• Lecture 13 The Chain Rule
• Lecture 14 Derivatives of Inverse Functions
• Lecture 15 Implicit Differentiation
• Lecture 16 Related Rates
• Lecture 17 Infinite Limits
• Lecture 18 Identifying Extrema
• Lecture 19 Families of Functions
• Lecture 20 Global Extrema
• Lecture 21 Applied Optimization
• Lecture 22 Determining Distance Traveled from Velocity
• Lecture 23 Riemann Sums
• Lecture 24 The Definite Integral
• Lecture 25 The Fundamental Theorem of Calculus
• Lecture 26 Constructing Accurate Graphs of Antiderivatives
• Lecture 27 FTC II
• Lecture 28 Substitution

Desmos Demos

A few years ago, I made some Desmos worksheets to supplement the slides above. You can find them below.

Note that while the section numbers have been updated to be consistent with the second edition of Active Calculus, many of the Desmos graphs are uneditable snapshots, and so the Desmos graphs in Sections 3.1–3.6 have numbers which are not consistent with the labels below.

Section 1.1

• Example 1.1 A: Tossing a ball
• Activity 1.1.2
• Activity 1.1.3

Section 1.2

• Example 1.2.1 Limit Failure
• Example 1.2.2 Table/Algebra
• Activity 1.2.2

Section 1.3

• Example 1.3.1 Secant lines
• Activity 1.3.3 Water balloon
• Activity 1.3.4 Population of AZ city

Section 1.4

• Example 1.4.1 Graphing the Derivative

Section 1.5

• Example 1.5.1 Comparing Difference Quotient and Central Difference

Section 1.6

• Example 1.6.1 Rates of change of rates of change

Section 1.7

• Example 1.7.1 Left and Right-hand limits
• Activity 1.7.2
• Example 1.7.2 Continuous vs Differentiable

Section 1.8

• Preview Activity 1.8.1 Parabola and Tangent Line
• Example 1.8.1 Local linearization of \(\sin(x)\)

Section 2.1

• Activity 2.1.4a \(h(z) = \sqrt{z}+\frac{1}{z}\) and tangent line
• Activity 2.1.4c \(p\left(x\right)=3x^{4}-2x^{3}+7x^{2}-x+12\) and tangent line

Section 2.2

• Activity 2.2.2 Sine and its tangents
• Activity 2.2.3 Cosine and its tangents

Section 2.4

• Activity 2.4.4 e

Section 2.5

• Activity 2.5.4 ab

Section 2.7

• Example 2.7.1
• Activity 2.7.2
• Activity 2.7.3

Section 3.2

• Preview Activity 3.2.1
• Example 3.2.1 Limits with infinity

Section 3.3

• Example 3.3.1 Absolute and Relative Extrema
• Example 3.3.2 First/Second Derivative Test
• Activity 3.3.4

Section 3.4

• Preview Activity 3.4.1
• Activity 3.4.2
• Activity 3.4.3
• Activity 3.4.4

Section 3.5

• Preview Activity 3.5.1
• Activity 3.5.2
• Activity 3.5.3

Section 3.6

• Activity 3.6.4

Section 4.1

• Area under a nonconstant velocity curve
• Activity 4.1.3 Tossing a ball
• Activity 4.1.4

Section 4.2

• Activity 4.2.3

Section 4.3

• Example 4.3.1 Interpreting the Definite Integral
• Example 4.3.2 Calculating a Definite Integral
• Activity 4.3.2
• Activity 4.3.4

Section 4.4

• Preview Activity 4.4.1
• Activity 4.4.2 Calculating Definite Integrals with Antiderivatives
• Activity 4.4.4 Total Change

Section 5.1

• Activity 5.1.2
• Activity 5.1.3
• Activity 5.1.4

Section 5.2

• Activity 5.2.2
• Activity 5.2.3