Brooks Emerick

mat 181 — Calculus

Spring 2024 — Sections 050 and 070

Course Materials:

• Syllabus (updated Jan 22 at 1:05 PM)

• Schedule (updated Jan 22 at 1:05 PM)

WebWork:

• WeBWork Login

• WeBWork Support

lecture notes:

• Trig Review — Unit Circle

• Chapter 1 — A Function Primer

• Chapter 2 — Limits

• Chapter 3 — Differentiation (Part 1)

• Chapter 3 — Differentiation (Part 2)

• Chapter 4 — Applications of the Derivative

• Chapter 5 — Integration

Videos and Desmos:

• Using GeniusScan to Upload Homework to D2L

• Riemann Sums in Desmos

• Video Lecture for April 23

Worksheets:

• S.1.1: Prerequisites and Functions (Solutions)

• S.1.2: Function Repertory (Solutions)

• S.1.3: Transformations and Combinations (Solutions)

• S.1.4: Inverse Functions (Solutions)

• S.2.2.P1: Limits all Around the Plane (Solutions)

• S.2.2.P2: Limits all Around the Plane (Solutions)

• S.2.4.P1: Determining Limits of Functions (Solutions)

• S.2.4.P2: Other Important Limits (Solutions)

• S.2.5.P1: Continuity (Solutions)

• S.2.5.P2: Continuity (Solutions)

• S.2.1: Rates of Change and Tangents (Solutions)

• S.2.6.P1: The Derivative at a Point (Solutions)

• S.2.6.P2: The Derivative Function (Solutions)

• S.3.1: Differential Notation (Solutions)

• S.3.2.P1: Derivatives of Polynomials and Exponential Functions (Solutions)

• S.3.2.P2: Derivatives of Products and Quotients (Solutions)

• S.3.3: Derivatives of Trig Functions (Solutions)

• S.3.4: Chain Rule (Solutions)

• S.3.5: Implicit Differentiation (Solutions)

• S.3.6: Derivatives of Inverse Functions (Solutions)

• S.4.1: Extreme Values of Functions (Solutions)

• S.4.2: Mean Value Theorem (Solutions)

• S.4.3.P1: Monotonicity and First Derivative Test (Solutions)

• S.4.3.P2: Concavity and Second Derivative Test (Solutions)

• S.4.4: L’Hopital’s Rule (Solutions)

• S.4.6: Optimization (Solutions)

• S.4.7: Antiderivatives (Solutions)

• S.5.1.P1: Areas, Distances, and Riemann Sums (Solutions)

• S.5.1.P2: Limit of a Riemann Sum (Solutions)

• S.5.2: The Definite Integral (Solutions)

• S.5.3: Fundamental Theorem of Calculus (Solutions)

• S.5.4.P1: Indefinite Integrals and U-Substitution (Solutions)

• S.5.4.P2: More U-Substitution (Solutions)

• S.5.5: U-Substitution on Definite Integrals and Symmetry (Solutions)

Problem Sets:

• Problem Set I (Solutions)

• Problem Set II (Solutions, Desmos Graph)

• Problem Set III (Solutions)

• Problem Set IV (Solutions, Desmos Graph 1, Desmos Graph 2)

• Problem Set V (Solutions)

• Problem Set VI (Solutions)

• Problem Set VII (Due Fri Apr 26 by 11:59 PM)

• Problem Set VIII (Due Fri May 3 by 11:59 PM)

Exams:

• Exam I (Solutions)

• Exam II (Solutions 1, Solutions 2)

• Exam III (Solutions)