# Calculus and Analytical Geometry (MTCE1013)

None

##### Recommended Book(s)

Calculus And Analytic Geometry, Addison Wesley, 9th Edition

##### Reference Book(s)

Calculus, Schum’s Series, Latest Edition

Calculus And Analytic Geometry, H.Antom, Latest Edition

## Course Objectives

1. To learn fundamentals of mathematics, calculus and analytical geometry. 2. To enable students to apply the ideas to solve problems of practical nature.

## Course Learning Outcomes (CLO)

 CLO:1            Have knowledge related to the fundamentals of calculus and analytical geometry. CLO:2            Understand the differentiation integration and their applications. CLO:3            Apply the acquired knowledge to solve problems of practical nature.

## Complex Numbers

• Basic operations

• Graphical representations

• Polar and exponential forms of complex numbers

• De’moivre’s theorem with applications

## Functions

• Hyperbolic functions and their graphical representation

• Hyperbolic and trigonometric identities and their relationship

• Exponential functions

## Differentiation

• Differentiation and successive differentiation and its application to rate, speed and acceleration

• Leibritze’s theorem and its applications

• Equations of tangents and normals, curvature

• Radius and centre of curvature

• Maxima and minima of function of one variable and its applications

• Convexity and concavity

• Points of inflexion

• Concept of infinite series

• Taylor’s and mclaurin’s series and expansion of functions

• Errors and approximations and limiting values of functions

## Partial Differentiation

• Partial differential coefficient and chain rule

• Partial differentiation of an implicit function

• Total differential

• Euler’s theorem

• Applications to small errors and approximations

• Statement of taylor’s theorem of two independent variable and its applications

## Integral Calculus

• Standard integrals

• Function of a linear function

• Integration by substitution, by partial fractions and by parts

• Integration of trigonometric functions

• Definite integrals and their properties and reduction formulae

• Curve tracing in rectangular and polar coordinates

## Integration Applications

• Volumes of solids of revolution

• Centroid of a plane figure

• Centre of gravity of a solid of revolution

• Lengths of curves

• Surface revolution

• Rules of pappus

• Moment of inertia

• Parallel axes theorem

• Perpendicular axes theorem

• Second moment of area

• Composite figures

• Centres of pressure and depth of centre of pressure

## Analytical Solid Geometry

• Rectangular co-ordinate systems in three dimensions

• Direction cosines

• Plane (straight line) and sphere

## Mapping of CLOs to Program Learning Outcomes

 CLO’s CLO-1 (Fundamental  Knowledge) CLO-2  (Understand Application) CLO-3  (Skill to Solve Problems) PLO’s PLO-1 (Engineering Knowledge) PLO-2 (Problem Analysis) √ √ √ PLO-3 (Design/Development of Solutions) PLO-4 (Investigation) PLO-5 (Modern Tool Usage) PLO-6 (The Engineer and Society) PLO-7 (Environment and Sustainability) PLO-8 (Ethics) PLO-9 (Individual and Team work) PLO-10 (Communication) PLO-11 (Project Management) PLO-12 (Lifelong Learning)

## Mapping of CLOs to Assessment Modules

 CLOs CLO:1 CLO:2 CLO:3 Assessment Modules Assignments (20-25%) √ √ Quizzes (15-20%) √ √ Midterm Exam (20%) √ √ Final Exam (40-45%) √ √ √