# Engineering Mathematics by V.P. Mishra: A Must-Have for Every Engineer - Barnes & Noble

# Engineering Mathematics by V.P. Mishra: A Comprehensive Textbook for Engineering Students - ## Introduction - What is engineering mathematics and why is it important? - Who is V.P. Mishra and what are his credentials? - What are the main features and benefits of his textbook? - ## Overview of the Book - How is the book organized and structured? - What are the topics and subtopics covered in each chapter? - How are the concepts explained and illustrated with examples and exercises? - ## Chapter 1: Differential Calculus - What are the basic concepts and rules of differentiation? - How to apply differentiation to engineering problems such as optimization, rate of change, and curve sketching? - What are the special functions and techniques of differentiation such as implicit, logarithmic, exponential, and inverse trigonometric functions? - ## Chapter 2: Integral Calculus - What are the basic concepts and rules of integration? - How to apply integration to engineering problems such as area, volume, work, and average value? - What are the special functions and techniques of integration such as integration by parts, substitution, partial fractions, and trigonometric identities? - ## Chapter 3: Differential Equations - What are differential equations and how to classify them? - How to solve first-order differential equations using various methods such as separation of variables, integrating factors, exact equations, and linear equations? - How to solve higher-order differential equations using various methods such as homogeneous equations, undetermined coefficients, variation of parameters, and Cauchy-Euler equations? - ## Chapter 4: Series and Sequences - What are series and sequences and how to represent them using sigma notation? - How to test the convergence and divergence of series and sequences using various criteria such as ratio test, root test, comparison test, and alternating series test? - How to find the sum of infinite series using various formulas such as geometric series, arithmetic series, telescoping series, and power series? - ## Chapter 5: Complex Analysis - What are complex numbers and how to perform arithmetic operations on them using rectangular and polar forms? - How to plot complex numbers on the complex plane and find their modulus and argument? - How to use De Moivre's theorem and Euler's formula to find the roots and powers of complex numbers? - ## Chapter 6: Linear Algebra - What are matrices and vectors and how to perform arithmetic operations on them using addition, subtraction, multiplication, scalar multiplication, and transpose? - How to find the determinant, inverse, rank, trace, eigenvalues, and eigenvectors of a matrix using various methods such as cofactor expansion, row reduction, characteristic equation, and diagonalization? - How to solve systems of linear equations using various methods such as Gaussian elimination, matrix inversion, Cramer's rule, and matrix factorization? - ## Chapter 7: Vector Calculus - What are vector functions and how to differentiate and integrate them using chain rule, product rule, quotient rule, and fundamental theorem of calculus? - How to find the arc length, curvature, torsion, tangential and normal components of a vector function using various formulas such as arc length formula, curvature formula, torsion formula, TNB frame, etc.? - How to use vector calculus to study scalar fields and vector fields using various concepts such as gradient, divergence, curl, directional derivative, line integral, surface integral, volume integral, Green's theorem, Stokes' theorem, Divergence theorem, etc.? - ## Chapter 8: Fourier Analysis - What are Fourier series and how to find them for periodic functions using trigonometric functions or complex exponentials? - How to use Fourier series to approximate non-periodic functions using half-range expansions or odd/even extensions? - How to use Fourier transform to convert functions from time domain to frequency domain or vice versa using various properties such as linearity, scaling, shifting, convolution, modulation, etc.? - ## Chapter 9: Laplace Transform - What is Laplace transform and how to find it for various functions using definition or tables of common transforms? - How to use Laplace transform to solve differential equations or integral equations using various properties such as linearity, scaling, shifting, differentiation, integration, convolution, etc.? - How to use inverse Laplace transform to find the original function from the transform using partial fraction decomposition or residue theorem? - ## Chapter 10: Probability and Statistics - What are probability and statistics and how to use them to analyze data and make inferences? - How to use various concepts and tools of probability such as sample space, events, axioms of probability, conditional probability, Bayes' theorem, random variables, probability distributions, expectation, variance, etc.? - How to use various concepts and tools of statistics such as descriptive statistics, inferential statistics, hypothesis testing, confidence intervals, correlation, regression, etc.? - ## Chapter 11: Numerical Methods - What are numerical methods and why are they useful for solving engineering problems? - How to use various numerical methods for finding roots of equations such as bisection method, Newton-Raphson method, secant method, etc.? - How to use various numerical methods for solving differential equations such as Euler's method, Runge-Kutta method, predictor-corrector method, etc.? - ## Chapter 12: Optimization Techniques - What are optimization techniques and how to use them to find the optimal solution for engineering problems? - How to use various optimization techniques for unconstrained problems such as gradient descent method, Newton's method, conjugate gradient method, etc.? - How to use various optimization techniques for constrained problems such as Lagrange multipliers method, Kuhn-Tucker conditions, linear programming, etc.? - ## Conclusion - Summarize the main points and benefits of the book - Provide some feedback and suggestions for improvement - Encourage the readers to buy the book and learn more about engineering mathematics - ## FAQs - Who is the target audience of this book? - How can I access the solutions of the exercises in this book? - What are the prerequisites for reading this book? - How can I contact the author of this book? - Where can I buy this book?

## Engineering Mathematics By Vp Mishra

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