B.Tech Aerospace Engg

# Engineering Mathematics-I

Course ID
1AE1-01
Campus
IIMT University, Meerut
Level
Method
Lecture
Semester
One
Credit
40

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### Course Objective:

1. To develop the use of Integral Calculus techniques that is needed by engineers for practical applications.
2. To make the students appreciate the purpose of using Sequences and Series to solve engineering problems.
3. To familiarize the student with functions of Fourier Series. This is needed in many branches of engineering.
4. To make the students understand various techniques of Multivariable Calculus differentiation.
5. To acquaint the student with mathematical tools needed in evaluating Multivariable Calculus integration and their applications.
6. To gain knowledge on primary level of Engineering mathematics and its application that they would find useful in their disciplines.

#### Unit I

Sequence and Series of Real Numbers: sequence – convergence – limit of sequence – nondecreasing sequence theorem – sandwich theorem (applications) – L’Hopital’s rule – infinite series -convergence – geometric series – tests of convergence (nth term test, integral test, comparison test, ratio and root test) – alternating series and conditional convergence – power series.

#### Unit II

Differential Calculus: functions of one variable – limits, continuity and derivatives – Taylors theorem –
applications of derivatives – curvature and asymptotes – functions of two variables – limits and continuity – partial derivatives – differentiability, linearization, and differentials – extremum of functions – Lagrange multipliers.

#### Unit III

Integral Calculus: lower and upper integral – Riemann integral and its properties – the fundamental theorem of integral calculus – mean value theorems – differentiation under integral sign – numerical Integration – double and triple integrals – change of variable in double integrals – polar and spherical transforms – Jacobian of transformations.

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### Textbooks:

1. Stewart, J., Calculus: Early Transcendentals, 7th ed., Cengage Learning (2010).
2. Jain, R. K. and Iyengar, S. R. K., Advanced Engineering Mathematics, 4th ed., Alpha Science Intl. Ltd. (2013).

### References:

1. Greenberg, M. D., Advanced Engineering Mathematics, Pearson Education (2007).
2. James, G., Advanced Modern Engineering Mathematics, 3rd ed., Pearson Education (2005).
3. Kreyszig, E., Advanced Engineering Mathematics, 10th ed., John Wiley (2011).
4. Thomas, G. B. and Finney, R. L., Calculus and Analytic Geometry, 9th ed., Pearson Education (2003).

### Course Learning Outcomes:

Upon completion of the course, Students will be able to
CO 1. Use the Integral Calculus techniques methods for solving practical problems.
CO 2. Apply Sequences and Series tools in solving various application problems.
CO 3. Obtain Fourier Series ideas on several variable functions.
CO 4. Manipulate different methods of Multivariable Calculus differentiation in solving practical
problems.
CO 5. Appreciate Multivariable Calculus integration ideas in solving practical problems.
CO 6. Make use of mathematical ideas to solve the practical problems in the society.