# 21MAT11: Calculus & Differential Equations syllabus Chemistry Group 2021 Scheme

Calculus & Differential Equations detailed syllabus for Chemistry Group 2021 Scheme curriculum has been taken from the VTUs official website and presented for the Chemistry Group students. For course code, course name, duration, number of credits for a course and other scheme related information, do visit full semester subjects post given below.

For Chemistry Group 1st Sem scheme and its subjects, do visit Chemistry Group 1st Sem 2021 Scheme scheme. The detailed syllabus of calculus & differential equations is as follows.

Calculus & Differential Equations

#### Teaching Learning Process (General Instructions):

These are sample Strategies, which teachers can use to accelerate the attainment of the various course outcomes.

1. In addition to the traditional lecture method, different types of innovative teaching methods may be adopted so that the delivered lessons shall develop student’s theoretical and applied mathematical skills.
2. State the need for Mathematics with Engineering Studies and Provide real-life examples.
3. Support and guide the students for self-study.
4. You will also be responsible for assigning homework, grading assignments and quizzes, and documenting students’ progress.
5. Encourage the students for group learning to improve their creative and analytical skills.
6. Show short related video lectures in the following ways:
• As an introduction to new topics (pre-lecture activity).
• As a revision of topics (post-lecture activity).
• As additional examples (post-lecture activity).
• As an additional material of challenging topics (pre-and post-lecture activity).
• As a model solution of some exercises (post-lecture activity).

#### Module 1:

Differential Calculus – 1 Polar curves, angle between the radius vector and the tangent, angle between two curves. Pedal equations. Curvature and Radius of curvature – Cartesian, Parametric, Polar and Pedal forms. Problems.
Self-Study: Center and Circle of Curvature, Evolutes and Involutes. (RBT Levels: L1, L2 and L3 )

Teaching-Learning Process 1 Chalk and Talk Method / Power Point Presentation

#### Module 2:

Differential Calculus – 2 Taylor’s and Maclaurin’s series expansion for one variable (Statement only) – problems. Indeterminate forms-L’Hospital’s rule. Partial differentiation, total derivative-differentiation of composite functions. Jacobian and problems. Maxima and minima for a function of two variables. Problems.
Self-Study: Euler’S Theorem and Problems. Method of Lagrange Undetermined Multipliers With Single Constraint. (RBT Levels: L1, L2 and L3)

Teaching-Learning Process Chalk and Talk Method / Power Point Presentation

#### Module 4:

Ordinary Differential Equations of higher order Higher-order linear ODE’s with constant coefficients – Inverse differential operator, method of variation of parameters, Cauchy’s and Legendre homogeneous differential equations. Problems.
Self-Study: Applications to Oscillations of a Spring and L-C-R Circuits. (RBT Levels: L1, L2 and L3)

Teaching Learning Process Chalk and Talk Method / Power Point Presentation

#### Module 5:

Linear Algebra Elementary row transformation of a matrix, Rank of a matrix. Consistency and Solution of system of linear equations; Gauss-elimination method, Gauss-Jordan method and Approximate solution by Gauss-Seidel method. Eigenvalues and Eigenvectors-Rayleigh’s power method to find the dominant Eigenvalue and Eigenvector.
Self-Study: Solution of System of Equations By Gauss-Jacobi Iterative Method. Inverse of a Square Matrix By Cayley- Hamilton Theorem. (RBT Levels: L1, L2 and L3).

Teaching Learning Process Chalk and Talk Method / Power Point Presentation

#### Course Outcomes:

(Course Skills Set) After successfully completing the course, the student will be able to understand the topics.

• Apply the knowledge of calculus to solve problems related to polar curves and its applications in determining the bentness of a curve.
• Learn the notion of partial differentiation to calculate rate of change of multivariate functions and solve problems related to composite functions and Jacobian.
• Solve first-order linear/nonlinear ordinary differential equations analytically using standard methods.
• Demonstrate various models through higher order differential equations and solve such linear ordinary differential equations.
• Test the consistency of a system of linear equations and to solve them by direct and iterative methods.

#### Reference Books:

1. V. Ramana: “Higher Engineering Mathematics” McGraw-Hill Education, 11th Ed.
2. Srimanta Pal & Subodh C. Bhunia: “Engineering Mathematics” Oxford University Press, 3rd Reprint, 2016.
3. N.P Bali and Manish Goyal: “A textbook of Engineering Mathematics” Laxmi Publications, Latest edition.
4. C. Ray Wylie, Louis C. Barrett: “Advanced Engineering Mathematics” McGraw – Hill Book Co.Newyork, Latest ed.
5. Gupta C.B, Sing S.R and Mukesh Kumar: “Engineering Mathematic for Semester I and II”, Mc-Graw Hill Education(India) Pvt. Ltd 2015.
6. H.K.Dass and Er. Rajnish Verma: “Higher Engineering Mathematics” S.Chand Publication (2014).
7. James Stewart: “Calculus” Cengage publications, 7th edition, 4th Reprint 2019.

#### Web links and Video Lectures (e-Resources):

• http://.ac.in/courses.php?disciplineID=111
• http://www.class-central.com/subject/math(MOOCs)