Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Engineering Mathematics

## Index of the Lesson Plan

UNIT – I NUMBER THEORY – 12 HRS
PRELIMINARIES & DIVISIBILITY

L-1 Introduction, Conjectures, Theorems and Proofs
L-2 Well ordering Principle, Principle of mathematical induction –
strong and weak – problems
L-3 Primes and Composite numbers, Fibonacci numbers, Lucas
numbers - problems
L-4 Sigma notation, Product notation, Binomial co-efficients –
properties, problems
L-5 Greatest integer function – properties, problems
L-6 Computers exercises and review exercises
L-7 Divisibility, proper divisor, non-trivial divisor, properties of
divisibility, division algorithm
L-8 Common divisors, Greatest common divisor, properties of
Greatest common divisor, Greatest common divisor via
Euclid’s algorithm, Linear form of GCD, problems
L-9 Relatively prime numbers, Euclid’s lemma, pair wise relatively
primes - problems
L-10 Common multiple, LCM, properties of LCM
L-11 Decimal representation of integers, binary representation of
integers - problems
L-12 Computer exercises and review exercises

UNIT – II PRIMES & CONGRUENCES – 12 HRS

L-13 Theorems on Composite and prime numbers, Twin primes
L-14 Prime counting function, Asymptotic functions, prime number
theorem
L-15 Canonical factorization of a natural number, fundamental
theorem of arithmetic
L-16 Dirichlet’s theorem, Bertrand’s postulates, Goldbach’s conjectures,
problems
L-17 Test of Primality by trial division
L-18 Computer exercises and review exercises
L-19 Congruences and equivalence relations, equivalence class -
problems
L-20 Least positive residue, linear congruences - problems
L-21 Chinese remainder theorem and problems
L-22 Modular arithmetic: Fermat’s little theorem
L-23 Fermat’s last theorem (Statement only), Wilson’s theorem and
Fermat numbers
L-24 Computer exercises and review exercises

UNIT – III ARITHMETIC FUNCTIONS, PRIMITIVE ROOTS
& INDICES & QUADRATIC CONGRUENCES – 12 HRS

L-25 Arithmetic functions: sigma function, Tau function,
Summation function, Sum of divisiors function, numbers of
divisors function, problems
L-26 Multiplicative function, totally multiplicative function,
Dirichlet product – properties and theorems, perfect numbers
and Mersenne primes
L-27 Dirichelt inverse, Moebius function, Euler’s function, Euler’s
theorem
L-28 Primitive roots – Definition and properties, Primitive root
(mod m)
L-29 Index, Properties of indices – problems
L-30 Computer exercises and review exercises
L-31 Quadratic residue and non-residue (mod p)
L-32 Euler’s criterion, properties of the Legendre symbol - problems
L-33 Gauss Lemma and related theorems
L-35 Solution of quadratic congruences, Algorithm for solving
quadratic congruences (mod p) - problems
L-36 Computer exercises and review exercises

UNIT -IV THE VECTOR SPACE RN &
LINEAR TRANSFORMATIONS – 12 HRS

L-37 Introduction to vectors, zero vector, Negative vector, Subtraction,
Column Vectors
L-38 Dot Product, Norm, Angle and Distance, Norm of a Vector in Rn
L-39 Angle between Vectors, Distance between Points, Introduction to
Linear Transformations
L-40 Composition of Matrix Transformations.
L-41 Linear Transformations, Kernel and Range Terminology
L-42 Transformations and systems of Linear Equations, Homogeneous
Equations, Non homogeneous Equations
L-43 Many Systems, Coordinate Vectors, Notation, Change of Basis
L-44 Isomorphisms, Matrix Representations of Linear Transformations
L-45 Importance of Matrix Representations, Relations between Matrix
Representations
L-46 Diagonal Matrix Representation of a Linear Operator
L-47 Diagonalization of a matrix-matrix partitioning
L-48 Problems on L-48 continued

UNIT -V NUMERICAL TECHNIQUES &
LINEAR PROGRAMMING – 12 HRS

L-49 Gaussian Elimination, Comparison of Gauss-Jordan and Gaussian
Elimination
L-50 Method of LU Decomposition, Construction of an LU
decomposition of a Matrix
L-51 Practical Difficulties in solving Systems of Equations, The
Condition Number of a Matrix
L-52 Pivoting and Scaling Techniques
L-53 Iterative methods for solving systems of Linear Equations, Jacobi
Method
L-54 Gauss-Siedel Method
L-55 Eigen values by Iteration, Connectivity of Networks
L-56 Deflation Accessibility Index of a Network
L-57 A Geometrical Introduction to Linear Programming, A Linear
Programming Problem
L-58 Minimum Value of a Function, Discussion of the Method
L-59 The simplex Method, Geometrical Explanation of the Simplex
Method
L-60 Problems on L-59 continued

## SYLLABUS FOR TESTS

 Test – I  Unit I: Number Theory  Unit II: Primes & Congruences Lesson Numbers L-1 to L-20 Test – II  Unit II: Primes & Congruences  Unit III: Arithmetic Functions, Primitive roots & Indices & Quadratic Congruences L-21 to L-36 Test – III  Unit IV: The vector space and Linear Transformation  Unit V: Numerical Techniques & Linear Programming L-37 to L-60