MAT 120 (lab)
Mathematica
Problem Sheet 1
Mathematical Functions: Basic Arithmetic and Elementary Functions
1. Write down the following expressions in mathematica and get the simplified form
5 9 7
8 5
3
a) 5 + + 8
7
100
2 10 63 64 4
b)
5 + 8 + 27
3
1
MAT 120 (Lab)
Mathematica
Problem Sheet 2
Algebraic Computation: Basic Algebra & Formula Manipulation
1. Write down the following algebraic expressions in mathematica:
3
x
2
a) sin
b) sin cos 1
x
c)
tan e ln cot
2. Find the value of the expression 1a)
MAT 120 (lab)
Mathematica
Problem Sheet 3
Building Functions
1. Build a function which takes a value x as an argument and gives the value of
a) e x sin( x)
b) ln(e x + e x )
2. Build a function which takes two values x and y as arguments and gives the
1 y
MAT 120 (Lab)
Mathematica
Problem Sheet 4
Graphics and Sound: 2D Plot, ContourPlot, PolarPlot, ParametricPlot
1. a) Plot the curve of following relation:
y = x 2 for 1 x 1
b) Label the axes
c) Add grid lines parallel to Y axis at an interval of 0.4 and gr
MAT 120 (lab)
Mathematica
Problem Sheet 5
List and Matrices: List, Table
1. a) Define a list, A = cfw_4, 16, 81, 64
b) Find a list, B whose elements are square root of the elements of A
c) Find the 3rd element of A and 4th element of B. Then add them
2. D
MAT 120 (lab)
Mathematica
Problem Sheet 6
Calculus: Limit, Derivative, Integration and Taylors series
1. Find out the following limit:
sin x
x 0
x
i) lim
ii) lim
x 3
x 3 5x
x 3 4 x 15
iii) lim
x 2 x 3 3 x 2
x 3
2. Find out the first, second and third deri
MAT 120 (lab)
Mathematica
Problem Sheet 7
1. Solve the differential equation
dy
= sin 5 x
dx
2. a) Solve the equation for y as a function of x
x2
dy
= y yx
dx
b) Find a special solution of the above mentioned equation for the following initial value
y (1)
MAT 120
Practice Sheet for Integral Calculus
From Calculus by Howard Anton (10th Edition)
5.2
5-36 Indefinite Integral
5.3
1-65 Integration by Substitution
5.4
27-30, 35-48 The definition of Area as a limit; Sigma notation
5.5
13-18, 25-28, 37, 38 The def