Course Outline

Course Outline / SyllabusCourse Title: PLANE and SPHERICAL TRIGONOMETRY Course Code: Math 2Pre-Requisite: Math 1 Credits: 3Total Hours: 54 hours

Course Description:

This course focuses entirely on plane trigonometry. The six trigonometric functions which are defined in terms of ratios are used routinely in calculations made by surveyors and navigators. Trigonometric functions also have applications in the physical and life sciences.Procedure using trigonometric tables and those using a calculator are included as needed to solve problems.Triangle solution problems, trigonometric identities, and trigonometric equations require knowledge of elementary algebra.

Course Objectives:

At the end of the semester, the students should be able to:1. define trigonometric functions2. enumerate the application of trigonometry3. evaluate trigonometric functions4. graph trigonometric functions5. solve equation involving trigonometric function6. solve problems on the application of trigonometric functions to geometry

Course Outline:

1. INTRODUCTION1.1 Definition1.2 Plane Angles1.2.1 . vertex1.2.2. initial 1.2.3. terminal1.2.4. positive angle1.2.5. negative angle1.3 Measures of angles1.3.1. degrees1.3.2. radians/radian measure1.4 Arc length1.5 Area of a sector

2. TRIGONOMETRIC FUNCTIONS2.1 Coordinate in a Plane

3. TRIGONOMETRIC FUNCTIONS OF AN ACUTE ANGLE3.1 Trigonometric functions of an acute angle3.2 Functions of complementary angles3.3 Finding the other functions of an acute angle when one function is given3.4 Angles with negative measures

3.5 Reduction Formulas3.6 Functions of Special angles (30, 60, 90 degrees)3.7 Applications of Special angles3.8 Interpolation3.9 Practical applications3.9.1. angle of elevation3.9.2. angle of depression3.9.3. bearing

4. SOLUTIONS OF OBLIQUE TRIANGLE4.1 The four cases4.2 Laws of Sines4.3 Solution of Case I4.4 Solution of Case II4.5 Laws of Cosines4.6 Solution of Case III4.7 Solution of Case IV

5. GRAPHIC REPRESENTATIONS OF THE TRIGONOMETRIC FUNCTIONS5.1 graphs of sin x and cos x5.2 graphs of tan x, cot x, sec x, csc x

6. TRIGONOMETRIC FORMULAS AND IDENTITIES6.1 Fundamental Identities6.2 Proving Trigonometric Identities

7. Inverse Trigonometric Functions

8. Trigonometric Equations

Course Requirements:

a. Class Standing (60%): assignments, quizzes, problem sets, recitation/board works, seat works, attendanceb. Examinations (40%)

Textbook: Plane and Spherical Trigonometry by Paul Rider

References:1. Schaum’s outline Series-Trigonometry2. Algebra and Trigonometry with application3. Holtmath 124. Modern Algebra and Trigonometry

Prepared by:

RAFFY H. DIOPIDOInstructor

Course Title: INTEGRAL CALCULUS Pre-Requisite: Differential CalculusCredit: 3Total Hours: 54 hours

Course Description:

Integral calculus is the continuation of Differential Calculus. It deals with definite and indefinite integrals and their properties. It covers the different integral properties.

Course Objectives:

At the end of the semester, the students should be able to:1. apply the properties of definite and indefinite integrals2. perform integration by using the appropriate method of integration

Course Outline:

I. INTEGRATION1.1 Antiderivatives and the indefinite integral1.2 The general formula for integration1.3 Area and the fundamental theorem of calculus1.4 The area of a region between two curves1.5 The definite integral as the limit of a sum

II. EXPONENTIAL AND LOGARITHMIC FUNCTIONS2.1 Integration of Exponential Functions2.2 Integration of Logarithmic Functions

III. TECHNIQUES OF INTERGRATION2.1 Integration by Substitution2.2 Integration by Parts2.3 Partial functions2.4 Numerical Integration2.5 Improper Integrals

IV. FUNCTIONS OF SEVERAL VARIABLES4.1 The Three-Dimensional Coordinate System4.2 Surfaces in Space4.3 Partial Derivatives4.4 Double Integrals and Area in the Plane


a. Class Standing (60%): assignments, quizzes, problem sets, recitation/board works, seat works, attendanceb. Periodical Examinations (40%)

Textbook: Brief Calculus

References:

1.Differential and Integral Calculus2. Calculus and Analytic Geometry3. Brief Calculus for Management and the Life and Social Sciences4. Applied Calculus

Prepared by:


Course Name: ADVANCED ALGEBRA

Course Description

Matrices and determinants; arithmetic and geometric series; solution sets of different types of inequalities and systems involving quadratics; solution of linear equations using determinants and matrices.

Credits: 3Number of Contact Hours per Week: 3 hours lecture

Prerequisites: College Algebra

Course Objectives:

After completing this course, the student must be able to:1. Determine the solution sets of inequalities;2. Determine the solution sets of systems involving quadratics;3. Use the manipulative and analytical skills acquired in Objective 2 to solve word problems;4. Operate and manipulate matrices and determinants;5. Solve systems of linear equations using matrices and determinants; and6. Determine the indicated sum of the elements in an arithmetic and geometric sequence.

Course Outline1. Inequalities1.1. Linear, Quadratic, and Polynomial Inequality1.2. Linear Inequalities with Absolute Value2. Ratio, Proportion, and Variation3. Determinants3.1. Expansion by Minors3.2. Solution of Linear Systems by Cramer’s Rule4. Matrices4.1. Identity Matrix4.2. Cofactor Matrix4.3. Transpose of a Matrix4.4. Adjoint Matrix4.5. Inverse of a Matrix4.6. Algebra on Matrices (Sum and Difference, Scalar Multiplication,Matrix Multiplication)4.7. Solution of Linear Systems Using Matrices5. Sequence and Series5.1. Arithmetic and Geometric Means5.2. Arithmetic and Geometric Sequences5.3. Arithmetic and Geometric Series5.4. Infinite Series6. Combinatorial Mathematics6.1. Sequences6.2. The Factorial of a Number6.3. Fundamental Principles of Counting, Permutation, and Combination6.4. Binomial Theorem6.5. Mathematical Induction

Laboratory Equipment: None



References:

Dugopolski, Mark. College Algebra, 3rd ed. Addison-Wesley, 2002.Leithold, Louis. College Algebra and Trigonometry. Massachusetts: Addison-Wesley, 1989.

Prepared y:


Course Name: SOLID MENSURATION

Course DescriptionConcept of lines and planes; Cavalieri’s and Volume theorems; formulas for areas of plane

figures, volumes for solids; volumes and surfaces areas for spheres, pyramids, and cones; zone, sector and segment of a sphere; theorems of Pappus.

Number of Units for Lecture and Laboratory: 3 units lecture

Number of Contact Hours per Week: 3 hours lecture

Prerequisite: College Algebra, Plane and Spherical Trigonometry

Course ObjectivesAfter completing this course, the student must be able to:

1. Compute for the area of plane figures;2. Compute for the surface areas and volumes of different types of solids; and3. Determine the volumes and surface areas of solids using other methods such as the theorems of Pappus.

Course Outline1. Plane Figures1.1. Mensuration of Plane Figures2. Lines and Planes in Space2.1. Typical Proofs of Solid Geometry2.2. Angles3. Solids for which V = Bh3.1. Solid Sections3.2. Cubes3.3. Rectangular Parallelopiped3.4. Cavalieri’s Theorem3.5. Volume Theorem3.6. Prism3.7. Cylindrical Surface3.8. Cylinder (Circular and Right Circular)4. Solids for which V = Bh .4.1. Pyramids4.2. Similar Figures4.3. Cones4.4. Frustum of Regular Pyramid4.5. Frustum of Right Circular Cone5. Sphere5.1. Surface Area and Volume5.2. Zone5.3. Segment5.4. Sector6. Theorems of Pappus



References: Kern, Willis F. and James R. Bland. Solid Mensuration, 2nd ed. New York: JohnWiley & Sons, Inc.

Prepared by:


Course Name: DIFFERENTIAL CALCULUS

Course DescriptionBasic concepts of calculus such as limits, continuity and differentiability of functions;

differentiation of algebraic and transcendental functions involving one or more variables; applications of differential calculus to problems on optimization, rates of change, related rates, tangents and normals, and approximations; partial differentiation and transcendental curve tracing.



Prerequisites: Advanced Algebra, Analytic Geometry, Solid Mensuration


1. Have a working knowledge of the basic concepts of functions and limits;2. Differentiate algebraic and transcendental functions with ease;3. Apply the concept of differentiation in solving word problems involving optimization, related rates, and approximation; and4. Analyze and trace transcendental curves.

Course Outline 1. Functions1.1. Definitions1.2. Classification of Functions1.3. Domain and Range of a Function1.4. Graph of a Function1.5. Functional Notation1.6. Evaluation of a Function1.7. Combinations of Functions1.8. One-Valued and Many-Valued Functions1.9. Odd and Even Functions1.10. Special Function Types1.11. Functions as Mathematical Models2. Continuity2.1. Definition2.2. Properties of Continuous Functions3. Limits3.1. Notion of a Limit3.2. Definition3.3. Properties of Limits3.4. Operations with Limits3.5. Evaluation of Limits3.6. One-Sided Limits3.7. Unbounded Functions4. The Derivative4.1. Notion of the Derivative4.2. Definition4.3. Determination of the Derivative by Increments4.4. Differentiation Rules5. The Slope5.1. Definition of Slope as the Derivative of a Function5.2. Determination of the Slope of a Curve at a Given Point6. Rate of Change6.1. Average Rate of Change

6.2. Instantaneous Rate of Change7. The Chain Rule and the General Power Rule8. Implicit Differentiation9. Higher-Order Derivatives10. Polynomial Curves10.1. Generalities About Straight Lines10.2. Tangents and Normal to Curves10.3. Extrema and the First Derivative Test10.4. Concavity and the Second Derivative Test10.5. Points of Inflection10.6. Sketching Polynomial Curves11. Applications of the Derivative: Optimization Problems12. Applications of the Derivative: Related Rates13. The Differential13.1. Definition13.2. Applications of the Differential—Comparison of x and dx13.3. Error Propagation13.4. Approximate Formulas14. Derivatives of Trigonometric Functions14.1. Elementary Properties14.2. Definition14.3. Graphs of Trigonometric Functions14.4. Applications15. Derivatives of Inverse Trigonometric Functions15.1. Elementary Properties15.2. Definition15.3. Graphs of Inverse Trigonometric Functions15.4. Applications16. Derivatives of Logarithmic and Exponential Functions16.1. Elementary Properties16.2. Definition16.3. Graphs of Logarithmic and Exponential Functions16.4. Applications17. Derivatives of Hyperbolic Functions17.1. Elementary Properties17.2. Definition17.3. Graphs of Hyperbolic Functions17.4. Applications18. Solution of Equations18.1. Newton’s Method of Approximation18.2. Newton-Raphson Law19. Transcendental Curve Tracing19.1. Logarithmic and Exponential Functions20. Parametric Equations21. Partial Differentiation



References:

Ellis, Robert and Benny Gulick. Calculus with Analytic Geometry. Harcourt Brace Jovanovich, 1990.Farlow, Stanley J. Calculus and Its Application. McGraw-Hill Publishing, 1990.

Leithold, Louis. The Calculus, 7th ed. Addison-Wesley, 2001.

Prepared by:RAFFY H. DIOPIDOInstructor

Course Name PROBABILITY AND STATISTICS

Course DescriptionBasic principles of statistics; presentation and analysis of data; averages, median, mode;

deviations; probability distributions; normal curves and applications; regression analysis and correlation; application to engineering problems.



Prerequisite: College Algebra


1. Define relevant statistical terms;2. Discuss competently the following concepts:2.1. Frequency distribution2.2. Measures of central tendency2.3. Probability distribution2.4. Normal distribution2.5. Inferential statistics3. Apply accurately statistical knowledge in solving specific engineering problem situations.

Course Outline: 1. Basic Concepts1.1. Definition of Statistical Terms1.2. Importance of Statistics2. Steps in Conducting a Statistical Inquiry3. Presentation of Data3.1. Textual3.2. Tabular3.3. Graphical4. Sampling Techniques5. Measures of Central Tendency5.1. Mean5.2. Median5.3. Mode5.4. Skewness and Kurtosis6. Measures of Variation6.1. Range6.2. Mean Absolute Deviation6.3. Variance6.4. Standard DeviationCourse Specification BSCE 10/746.5. Coefficient of Variation7. Probability Distributions7.1. Counting Techniques7.2. Probability7.3. Mathematical Expectations7.4. Normal Distributions8. Inferential Statistics8.1. Test of Hypothesis8.2. Test Concerning Means, Variation, and Proportion8.3. Contingency Tables8.4. Test of Independence

8.5. Goodness-of-Fit Test9. Analysis of Variance10. Regression and Correlation



References:Sellers, Gene R. and Stephen A. Vardeman. Elementary Statistics, 2nd ed.Saunders College Publishing, 1982..

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