### Calculus and Analytical Geometry (MATH-101)

Calculus is a transition course to upper-division mathematics and computer science courses. Students will extend their experience with functions as they study the fundamental concepts of calculus: limiting behaviors, difference quotients and the derivative, Riemann sums and the definite integral, antiderivatives and indefinite integrals, and the Fundamental Theorem of Calculus.

Prerequisite

To succeed in this course you will need to be comfortable with  Algebra I (elementary algebra) and Algebra II (intermediate algebra).

Learning Outcomes

At the end of this course the student will be able to:

• calculate limits, derivatives, and integrals of various algebraic and trigonometric functions of a single variable
• understand  the basic concepts of differential and integral calculus.
• to analyze graphs of various functions of a single variable including transcendental functions.
• find area of regions by using integrals.
• solve integrals numerically.

Contents

1. Real Numbers and the Real Line, Coordinates, Lines, and Increments, Functions, Shifting Graphs, Trigonometric Functions.
2. Limits and Continuity: Rates of Change and Limits, Rules for Finding Limits, Target Values and Formal Definitions of Limits, Extensions of the Limit Concept, Continuity, Tangent Lines.
3. Derivatives: The Derivative of a Function, Differentiation Rules, Rates of Change, Derivatives of Trigonometric Functions, The Chain Rule, Implicit Differentiation and Rational Exponents.
4. Applications of Derivatives: Extreme Values of Functions, The Mean Value Theorem, The First Derivative Test for Local Extreme Values, Graphing with y‘ and y‘‘.
5. Integration: Indefinite Integrals, Integration by Substitution—Running the Chain Rule Backward, Estimating with Finite Sums, Riemann Sums and Definite Integrals, Prop-erties, Area, and the Mean Value Theorem. Substitution in Definite Integrals. Numerical Integration.
6. Applications of Integrals: Areas between Curves, Finding Volumes by Slicing, Volumes of Solids of Revolution—Disks and Washers. Cylindrical Shells. Lengths of Plan Curves, Areas of Surfaces of Revolution, Moments and Centers of Mass.
7. Transcendental Functions: Inverse Functions and Their Derivatives, Natural Logarithms, The Exponential Function, a^x and log_a( x), Growth and Decay, L'Hôpital's Rule, Relative Rates of Growth, Inverse Trigonometric Functions, Derivatives of Inverse Trigonometric Functions; Integrals. Hyperbolic Functions.
8. Conic Sections, Parameterized Curves, and Polar Coordinates: Conic Sections and Quadratic Equations. Classifying Conic Sections by Eccentricity. Quadratic Equations and Rotations. Parameterizations of Plan Curves. Calculus with Parameterized Curves. Polar Coordinates. Graphing in Polar Coordinates. Polar Equations for Conic Sections. Integration in Polar Coordinates.
9. Vectors and Analytic Geometry in Space, Vectors in the Plane Dot Products, Vector-Valued Function Cartesian (Rectangular) Coordinates and Vectors in Space. Dot Products. Cross Products. Lines and Planes in Space. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates.

Textbook(s)

• Calculus and Analytic Geometry by George B. Thomas and Ross L. Finney, Addison Wesley; 10th Edition (1995).
• Calculus and Analytical Geometry by Swokowski, Olinick and Pence, 6th Edition, (1994), Brooks/Cole Publishers.
• Calculus by Howard Anton, Irl C. Bivens, Stephen Davis ; 10th Edition (2012).
• Calculus with Analytic Geometry: Student Solution Manual by Howard Anton ; 5th Edition (1995)Linear Algebra:

Suggested Book(s)

• Calculus and Analytic Geometry by James Stewart; 7th Edition, Brooks/Cole Publishers (1995).

ASSESSMENT CRITERIA

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:  30

Final-Term Exam: 50

### Key Dates and Time of Class Meeting

Monday-Wednesday                                                                    2:00pm-3:30pm

Commencement of Classes                                                   October 26, 2020

Mid Term Examination                                                            December 28, 2020 to January 01, 2021

Final Term Examination                                                          March 01-05, 2021

Declaration of Result                                                              March 12, 2021