- Teacher: MHN De Silva
- Teacher: Dr. Yashika Jayathunga
- Teacher: MHN De Silva
- Teacher: Dr. Pushpa Malkanthi
B.Sc in Agricultural Sciences and Management
Descriptive Course Unit
Course Unit Title: Mathematics
|
Unit Code |
Credits |
Theory (hrs) |
Applications (hrs) |
Total hours |
|
AB 11012 |
2 |
15 |
30 |
45 |
Description of unit
This unit covers elementary concepts of algebra, basic operations and definitions that are used in other applications in Mathematics. It also covers the fundamentals of calculus and their applications in life science researches.
Intended learning outcomes (ILO)
To achieve this unit a learner must be able to
1) Obtain the knowledge in different number systems, skills in Solving simple linear equations and inequalities, Manipulating expressions with logarithms, indices and perform operations with radicals
2) Obtain the knowledge and skills in coordinate geometry and trigonometry
3) Obtain the knowledge to work with polynomial functions and apply them into different situations
4) Obtain the knowledge in limits and explain the continuity of functions
5) Obtain the knowledge and skills in calculus
6) Obtain the knowledge and skills in matrix algebra
Content
|
ILO 1 : Preliminaries |
|
Number systems |
|
Real number line, Real numbers, Integers, Natural Numbers, Rational and Irrational Numbers, order of operations |
|
Equations and Inequalities |
|
Rules of inequalities, solving liner equations and inequalities |
|
Exponents, Logs, Roots and Radicals |
|
Laws of logarithms, Laws of exponents, of indices, simplification of radical expressions, extraction of roots |
|
|
|
ILO 2: Coordinate Geometry and Preliminaries of Trigonometry |
|
Cartesian Plane |
|
rectangular coordinate system, ordered pairs and solutions to equations in two variables |
|
Equation of a straight line |
|
Liner distance between two points, Types of liner equations (point-point, point-line, y-intersect, x-intercept, x,y- intercept |
|
Working with linear equations |
|
Parallel equations, interceptions of two lines, perpendicular equations |
|
Other geometric shapes |
|
Circle on X-Y plane, Parabola, intersection of line and circle |
|
Preliminaries of trigonometry |
|
Concepts, Angles, Rules of Sine, Cosine, Tangent, Applications of Trigonometry |
|
|
|
ILO 3: Quadratic, Cubic and Higher Order Polynomials |
|
Quadratic Equations |
|
Properties: roots, intersections, turning points; Obtaining roots by factorization, completing square, using formula, Difference of squares and cubes |
|
Cubic and Higher order polynomials |
|
Properties, graphical presentation, estimation of approximate roots by graphical method |
|
|
|
ILO 4: Limits and continuity of functions |
|
Limits |
|
Definition of the limit, infinity on the x- axis· infinity on the y- axis, infinity on both axes |
|
Techniques of Limits |
|
Canceling a linear factor, non existence of limit, Difference of two squares, Combining the numerator, Multiplying by a unity factor, Factoring cubic polynomials, Substitution |
|
Continuity of functions |
|
Definition of Continuity, Types of Discontinuous Functions: the Step Function, the Jump Discontinuity · |
|
|
|
ILO 5: Differentiation |
|
Preliminaries |
|
The Concept and Definition of the Derivative (slope form and increment form), Differentiability, Calculation of the Derivative, ·Graphical Representation of the Derivative, Calculation of Derivatives from the Definition, Derivation of the First Principle of Derivatives |
|
Properties |
|
Linearity, Linear Combination Rule, Definition of Product Rule, Definition of the Quotient Rule, Definition of the Chain Rule (function of a function and composition version) |
|
Logarithmic |
|
Derivative of log functions, Derivative of exponential functions |
|
Trigonometric |
|
Derivatives of Trigonometric functions |
|
Higher Order |
|
Higher order derivatives, Total and partial derivatives, Implicit differentiation |
|
Curve sketching |
|
Definition of Minimum, Minimum and inflection points, Calculation of minimum number of coordinates of curve sketching |
|
Real World Applications |
|
Displacement, Velocity and Acceleration, Use in Basic Micro-economic models and theories |
|
|
|
ILO 5: Integration |
|
Introduction |
|
Relationship between integration and differentiation, derivation of general rule of integration |
|
Rules of integration |
|
Integral of a constant, power rule, standard table of integration, integration by parts, integration by substitution, partial fraction |
|
Area |
|
Evaluation of area under different functions, geometric shapes: circle, ellipse, sectoral area |
|
Volume |
|
Concept of volume, evaluation of volume of revolving solid, volume of sphere, volume of a revolving centoroid |
|
|
|
ILO 6: Matrix Algebra and Liner Systems |
|
Matrix Algebra |
|
Types of matrices, matrix operations: additions, subtraction, multiplication, transpose of a matrix, determinant of a matrix, inverse |
|
Linear Systems |
|
Two variable to many variable systems, solutions through inverse approach, Cramer’s rule |
Guidance
Course unit Delivery Method: Class room lectures
Time Schedule, Lecture Plan and Method of Evaluation of Course unit
Course Unit: Mathematics
Unite Code: AB 11012
|
Week |
Lessons |
Topics |
Scheduled Assignment/ Continuous Assessment |
|
01 |
01 |
Preliminaries |
|
|
02 |
02 |
Coordinate Geometry and Preliminaries of Trigonometry |
|
|
03 |
03 |
Quadratic, Cubic and Higher Order Polynomials |
Assignment 01 |
|
04 |
|
Quiz 01 |
Quiz 01 |
|
05 |
04 |
Limits and continuity of functions |
|
|
06 |
04 |
Differentiation |
|
|
07 |
04 |
Differentiation |
|
|
08 |
04 |
Differentiation |
|
|
09 |
04 |
Differentiation |
|
|
10 |
04 |
Differentiation |
Assignment 02 |
|
11 |
|
Quiz 02 |
Quiz 02 |
|
12 |
05 |
Integration |
|
|
13 |
05 |
Integration |
|
|
14 |
06 |
Matrix Algebra and Linear Systems |
|
|
15 |
06 |
Matrix Algebra and Linear Systems |
|
Method of Evaluation
a. Continuous Assessment
Total marks allocated: 30%
|
Type of Continuous Assessment |
After the lesson number |
Week Schedule |
Marks allocated from the total marks in % |
|
Assignment 01 |
03 |
03 |
10 |
|
Quiz 01 |
03 |
04 |
40 |
|
Assignment 02 |
04 |
10 |
10 |
|
Quiz 02 |
04 |
11 |
40 |
b. End semester Examination:
Total marks allocated: 70%
|
Method of Evaluation |
Ways of Evaluation |
Marks allocated |
|
End semester evaluation
|
MCQ paper (20 questions, Time allocation 30 minutes) :20% Essay type question paper (Time allocation 1 and ½ hours, 4 out of 5 questions): 80% |
70% |
References
Murray Spiegel and Robert Moyer, Schaum's Outline of College Algebra, Third Edition (Schaum's Outline Series, 2009), McGraw-Hill;
ISBN-10: 9780071635394 ISBN-13: 978-0071635394
Argres, F. and Ellott Mendelson, J. R. (2000): Calculus. McGraw-Hill, New York.
Monga, G. S. (1999): Mathematic for Management and Economics. Vikas Publishing House, New Delhi.
Ramsey, A. S. (1998): Elementary Calculus. The Cambridge University Press, London.
Thomas, G. B. and Finney, R. L. (1998): Calculus and Analytic Geometry. Addison-Weskly Publishing Company Inc.
ISBN-10: 0070419736
ISBN-13: 978-0070419735