Calculus and Analytical Geometry (MTME1013)
Prerequisite(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)
CLO1: Explain the ideas of rate of change and derivatives using the concept of limits and continuity. (C2)
CLO2: Apply the derivatives for solving different problems arising in engineering sciences. (C3)
CLO3: Use the techniques of integration for solving problems in integral calculus. (C3)
CLO4: 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
OneSided 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.
VectorValued Functions and Space Curves
ArcLength 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) 



