Calculus and Analytical Geometry (MTME1013)

Pre-requisite(s)

None

Recommended Book(s)

Calculus And Analytical Geometry By Thomas/Finney, 11th Edition

Reference Book(s)

Advanced Engineering Mathematics, By Erwin Kreyszig, 8th Edition

Calculus And Analytical Geometry, Schaum’s Series 

Course Objectives

The main aim of this course is to give students some basic ideas of calculus, which is the mathematics of motion. The purpose is not just making the students learn these ideas but to enable them to apply these ideas to solve problems of practical nature. The course will provide the students with the necessary tools to understand and formulate advanced mathematical concepts and an awareness of their relationship to a variety of problems arising in engineering and sciences. Students wishing to major in the sciences, engineering, or medicine are required to have a working knowledge of the calculus and its applications.

Course Learning Outcomes (CLO)

CLO-1: Explain the ideas of rate of change and derivatives using the concept of limits and continuity. (C2)

CLO-2: Apply the derivatives for solving different problems arising in engineering sciences. (C3)

CLO-3: Use the techniques of integration for solving problems in integral calculus. (C3)

CLO-4: Learn and use the vector calculus and analytical geometry in multiple dimensions. (C3)

Course Contents

Limits and Continuity – FourLectures

Introduction to Limits

Rates of Change and Limits

One-Sided Limits, Infinite Limits

Continuity, Continuity at a Point, Continuity on an interval

Differentiation – SixLectures

Definition and Examples

Relation Between Differentiability and Continuity

Derivative as slope, as rate of change (graphical representation).

The Chain Rule

Applications of Ordinary Derivatives

Integration – Five Lectures

Indefinite Integrals

Different Techniques for  Integration

Definite Integrals

Riemann Sum, Fundamental Theorem of Calculus

Area Under the Graph of a Nonnegative Function

Improper Integrals

Transcendental Functions– FiveLectures

Inverse functions

Logarithmic and Exponential Functions

Inverse Trigonometric Functions

Hyperbolic Functions and Inverse Hyperbolic Functions

More Techniques of Integration

Analytical Geometry – Ten Lectures

Three Dimensional Geometry

Vectors in Spaces

Vector Calculus

Directional Derivatives

Divergence, Curl of a Vector Field

Multivariable Functions

Partial Derivatives

Analytical Geometry – Ten Lectures

Conic Sections

Parameterizations of Plane Curves

Vectors in Plane, Vectors in space

Dot Products, Cross Products

Lines and Planes in Space

Spherical, Polar and Cylindrical Coordinates.

Vector-Valued Functions and Space Curves

Arc-Length and Tangent Vector

Curvature, Torsion and TNB Frame

Fubini’s Theorem for Calculating Double Integrals

AreasMoments and Centers of Mass

Triple Integrals, Volume of a Region in Space

Mapping of CLOs to Program Learning Outcomes

CLOs/PLOs

CLO:1

CLO:2

CLO:3

CLO:4

PLO:1 (Engineering Knowledge)

 

 

 

PLO:2 (Problem Analysis)

 

 

 

 

PLO:3 (Design Development of Solutions)

 

 

 

 

PLO:4 (Investigation)

 

 

 

 

PLO:5 (Modern Tool Usage)

 

 

 

 

PLO:6 (Engineer & Society)

 

 

 

 

PLO:7 (Environment and Sustainability)

 

 

 

 

PLO:8 (Ethics)

 

 

 

 

PLO:9 (Individual & Team Work)

 

 

 

 

PLO:10 (Communication)

 

 

 

 

PLO:11 (Project Management)

 

 

 

 

PLO:12 (Life Long Learning)