# VTU B.TECH Civil Engineering SEMESTER – III Syllabus For Additional mathematics – i PDF 2022

### Get Complete Lecture Notes for Additional mathematics – i on Cynohub APP

You will be able to find information about Additional mathematics – i along with its Course Objectives and Course outcomes and also a list of textbook and reference books in this blog.You will get to learn a lot of new stuff and resolve a lot of questions you may have regarding Additional mathematics – i after reading this blog. Additional mathematics – i has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Additional mathematics – i can be learnt easily as long as you have a well planned study schedule and practice all the previous question papers, which are also available on the CynoHub app.

All of the Topic and subtopics related to Additional mathematics – i are mentioned below in detail. If you are having a hard time understanding Additional mathematics – i or any other Engineering Subject of any semester or year then please watch the video lectures on the official CynoHub app as it has detailed explanations of each and every topic making your engineering experience easy and fun.

### Additional mathematics – i Unit One

#### 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.

### Additional mathematics – i Unit Two

#### Differential Calculus

Review of successive differentiation-illustrative examples. Maclaurin’s series expansions-Illustrative examples. Partial Differentiation: Euler’s theorem-problems on first order derivatives only. Total derivatives-differentiation of composite functions. Jacobians of order two-Problems.

### Additional mathematics – i Unit Three

#### 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-simple problems. Solenoidal and irrotational vector fields-Problems.

### Additional mathematics – i Unit Four

#### Integral Calculus

Review of elementary integral calculus. Reduction formulae for sinnx, cosnx (with proof) and sinmx cosnx (without proof) and evaluation of these with standard limits-Examples. Double and triple integrals-Simple examples.

### Additional mathematics – i Unit Five

#### Ordinary differential equations (ODE’s

Introduction-solutions of first order and first degree differential equations: exact, linear differential equations. Equations reducible to exact and Bernoulli’s equation.

### Additional mathematics – i Course 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.

### Additional mathematics – i 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 related area. • CO2: Use derivatives and partial derivatives to calculate 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.

### Additional mathematics – i Text Books

Higher Engineering Mathematics-B.S. Grewal

### Additional mathematics – i Reference Books

Engineering Mathematics N.P.Bali and Manish Goyal
Engineering Mathematics Vol.I Rohit Khurana

### Scoring Marks in Additional mathematics – i

Information about VTU B.Tech Additional mathematics – i was provided in detail in this article. To know more about the syllabus of other Engineering Subjects of JNTUH check out the official CynoHub application. Click below to download the CynoHub application.

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