ADDITIONAL MATHEMATICS – I (18MATDIP31)

ADDITIONAL MATHEMATICS – I 

(Mandatory Learning Course: Common to All Programmes)

(A Bridge course for Lateral Entry students under Diploma quota to BE/B. Tech. programmes)

Course Code:18MATDIP31 CIE Marks:40
SEE Marks:60
Teaching Hours/Week (L:T:P):(2:1:0) Credits:0
Exam Hours:03

Course Learning Objectives:

• To provide basic concepts of complex trigonometry, vector algebra, differential and integral calculus.
• To provide an insight into vector differentiation and first order ODE’s.

Module-1

Complex Trigonometry: Complex Numbers: Definitions and properties. Modulus and amplitude of a complex number, Argand’s diagram, De-Moivre’s theorem (without proof).
Vector Algebra: Scalar and vectors. Addition and subtraction and multiplication of vectors- Dot and Cross products, problems.

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Module-2

Differential Calculus: Review of elementary differential calculus. Polar curves –angle between the radius vector and the tangent pedal equation- Problems. Maclaurin’s series expansions, problems.
Partial Differentiation: Euler’s theorem for homogeneous functions of two variables. Total derivatives -differentiation of composite function. Application to Jacobians of order two.

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Module-3

Vector Differentiation: Differentiation of vector functions. Velocity and acceleration of a particle moving on a space curve. Scalar and vector point functions. Gradient, Divergence, Curl and Laplacian (Definitions only). Solenoidal and irrotational vector fields-Problems.

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Module-4

Integral Calculus: Review of elementary integral calculus. Statement of reduction formulae for
sin ,cos , sin  × cos and evaluation of these with standard limits-Examples. Double and triple integrals, problems.

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Module-5

Ordinary differential equations (ODE’s): Introduction-solutions of first order and first-degree differential equations: Variable Separable methods, exact and linear differential equations of order one. Application to Newton’s law of cooling.

Full Notes

Course Outcomes: At the end of the course the student will be able to:

• CO1: Apply concepts of complex numbers and vector algebra to analyze the problems arising in a related area.
• CO2: Use derivatives and partial derivatives to calculate the rate of change of multivariate functions.
• CO3: Analyze position, velocity, and acceleration in two and three dimensions of vector-valued functions.
• CO4: Learn techniques of integration including the evaluation of double and triple integrals.
• CO5: Identify and solve first-order ordinary differential equations.

Question paper pattern:

• The question paper will have ten full questions carrying equal marks.
• Each full question will be for 20 marks.
• There will be two full questions (with a maximum of four sub- questions) from each module.

Sl. No. Title of the Book Name of the Author/s Name of the Publisher Edition and Year

Textbook

1 Higher Engineering Mathematics B.S. Grewal Khanna Publishers 43rd Edition, 2015

Reference Books

1 Advanced Engineering Mathematics E. Kreyszig John Wiley & Sons 10th Edition, 2015
2 Engineering Mathematics Vol.I RohitKhurana Cengage Learning 2015

Softcopy Textbook Links:

1. ADVANCED ENGINEERING MATHEMATICS 10th ed ERWIN KREYSZIG Download Link

2. Higher Engineering Mathematics John Bird Download Link

3. CALCULUS EARLY TRANSCENDENTALS HOWARD ANTON & IRL BIVENS Download Link

4.  A Textbook of ENGINEERING MATHEMATICS-I  H.S. Gangwar Download Link

Hardcopy Textbook Links: