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

Course Outline (Fall Semester 2020)

• Course Title: Calculus and Analytical Geometry
• Course Code: MATH-101
• Credit Hours: 03
• Instructor: Memoona Nawaz
• Email: [email protected]

Introduction to Course:

Calculus and Analytical Geometry presents the essentials of Calculus and Analytical Geometry. The emphasis is on how to set up and solve calculus problems, that is, how to apply calculus.

Course Objectives:

• To provide foundation and basic ground for calculus and analytical geometry background.
• To enable the students to understand the principles of calculus and its application in solving engineering problems.

Course Learning Outcomes:

• Have knowledge related to the fundamentals of calculus and analytical geometry.
• Understand the differentiation integration and their applications.
• Apply the acquired knowledge to solve problems of practical nature.

Course Syllabus:

Real Numbers and the Real Line. Functions. Shifting Graphs, Trigonometric Functions. Limits and Continuity. Tangent Lines. Derivatives. Differentiation Rules. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation and Rational Exponents. Applications of Derivatives. Integration. Numerical Integration. Applications of Integrals. Transcendental Functions. Inverse Trigonomic Functions. Derivatives of Inverse Trigonometric Functions. Integrals. Hyperbolic Functions. Conic Sections, Parametrized Curves, and Polar Coordinates. Vectors and Analytic Geometry in Space.

Course Outline:

1. Real Numbers and the Real Line, Coordinates, Lines, and Increments, Functions, Shifting Graphs, Trigonometric Functions. [TB: Preliminaries]
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. [TB: Ch. 1]
3. Derivatives: The Derivative of a Function, Differentiation Rules, Rates of Change, Derivatives of Trigonometric Functions, The Chain Rule, Implicit Differentiation and Rational Exponents. [TB: Ch. 2]
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‘‘.  [TB: Ch.3]
5. Integration: Indefinite Integrals, Integration by Substitution—Running the Chain Rule Backward, Estimating with Finite Sums, Riemann Sums and Definite Integrals, Properties, Area, and the Mean Value Theorem. Substitution in Definite Integrals. Numerical Integration. [TB: Ch. 4]
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. [TB: Ch. 5]
7. Transcendental Functions: Inverse Functions and Their Derivatives, Natural Logarithms, The Exponential Function, ax and logax, Growth and Decay, L'Hôpital's Rule, Relative.
8. Rates of Growth, Inverse Trigonometric Functions, Derivatives of Inverse Trigonometric Functions; Integrals. Hyperbolic Functions. [TB: Ch. 6].
9. 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. [TB: Ch. 7, 9]..
10. 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. [TB: Ch. 9,10]

Textbook(s):

• Calculus and Analytic Geometry by George B. Thomas and Ross L. Finney, Addison Wesley; 10th Edition (1995) ISBN-10: 0201531747

Recommended Books:

•  ​Calculus by Howard Anton, Irl C. Bivens, Stephen Davis, Wiley; 10th Edition (2012), ISBN-10: 0470647728.
• Calculus with Analytical Geometry by S.M Yusuf, Latest Edition.

Reference Material:

• Calculus and Analytical Geometry by Swokowski, Olinick and Pence, 6th Edition, (1994), Brooks/Cole Publishers.
• Calculus by Howard Anton, Irl C. Bivens, Stephen Davis, Wiley; 10th Edition (2012), ISBN-10: 0470647728.
• Calculus with Analytic Geometry: Student Solution Manual by Howard Anton, Wiley; 5th Edition (1995). ISBN-10: 0471105899

Assessment Criteria:

• Mid-Term Exam:  30
• Final-Term Exam: 50
• Sessional: 20 (Assignment 05, Presentation 05, Attendance 05, Quiz 05)

Key Dates and Time of Class Meeting:

Program: BSSE (2020-2024)

Class: Self-Support (1st- Semester)

• Monday:                09:30 AM -11:00 AM
• Friday:                    09:20 AM -10:40 AM