Calculus+I

﻿**COURSE SYLLABUS**  ﻿ **MATH 119 - CALCULUS I**

 **Course Code:** MATH 119
 * Course Title:** Calculus I (Differential Calculus)
 * Intended for:** BSIT NW Second Year, BSCS SD Second Year, BSCS ND Second Year
 * Credit Units:** Three (3) Units
 * Pre-requisite:** Math 102 / Math 105

 **Course Description:**  This courser introduces to students the fundamentals of Calculus: limits, continuity and derivatives. This course assumes a thorough understanding of concepts on analytic geometry and trigonometry. The use of graphing calculators and computer algebra systems is highly encouraged.

**General Objective:** The course is intended to provide students with knowledge about the fundamentals of calculus. It enables the students to use the process of differentiation in solving problems. **Specific Objective:** At the end of the semester, students are expected to: 1. set up formulas showing the functional relation between the variables. 2. obtain the limits of more complicated functions which are assuming the indeterminate forms. 3. find the value or values of x for which the function is discontinuous. 4. sketch the graph of different functions and determine its vertical and horizontal asymptote. 5. find the derivative of the functions. 6. find the slope of a tangent to the curve at the given point. 7. find dy/dx (derivative) following the rules of differentiation. 8. determine dy/dx of composite functions using the chain rule. 9. use the inverse function rule to find dy/dx 10. give the higher derivatives of the given function. 11. differentiate implicitly. 12. find the equations of tangents and normals to the graph of the given point. 13. find the acute angle between the given curves 14. find the interval or intervals where the function is increasing or decreasing in the given interval. 15. find the value or values of x, for which the given function has a point of inflection. 16. obtain the values of x for which the curve of the given function has a point of inflection. 17. give the maximum, minimum of the inflection point of each curve. 18. use the process of differentiation as an application in solving problems related to maxima and minima, related rates and rectilinear motion. 19. determine the derivative of: 20. verify the three conditions of the hypothesis of Rolle’s Theorem are satisfied by the given function on the given interval and find the value of which <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">satisfies the conclusion of the theorem. 21. use the Mean Theorem in proving. 22. evaluate limits of a quotient of two functions when the numerator and denominator approach zero.
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">trigonometric functions
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">inverse trigonometric functions
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">logarithmic functions
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">exponential functions
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">hyperbolic functions
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">inverse hyperbolic functions

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">**Course Outline:**

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">University Mission & Vision 1 <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;"> <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">**Midterm Grading Period** <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;"> <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;"> The Derivative (18 hours) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;"> Graphing (18 hours) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">**Final Grading Period** <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;"> <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;"> Additional Derivative Topics (17 hours) <span style="font-family: Tahoma,Geneva,sans-serif;">
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px;"><span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">Rate of Change & Slope
 * Limits
 * The Derivative
 * Derivatives of Constants,Power Forms & Sums
 * Derivatives of Products and Quotients
 * Chain Rule: Power Form
 * Applications
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px;"><span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">Continuity & Graphs
 * First Derivative
 * Second Derivative & Graphs
 * Curve Sketching & Techniques
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">Optimization, Absolute Maxima and Absolute Minima
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px;"><span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">The Constant & Continuous Compound Interest
 * Derivatives of Logarithmic & Exponential Functions
 * Chain Rule: General Form
 * Implied Differentiation
 * Related Rates

<span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">**Methods of Teaching:** <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;"> <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Classroom discussion, discovery, investigation, application of softwares, GeoAlgebra, Sketchpad and Scientific Notebook. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">**Course Requirement/Assessments:**

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Quizzes, recitation / board works, assignments, problem sets, periodic exams (midterm/finals), reaction papers. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">**Criteria for Grading:** <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">The following shall be used as the basis for giving grades: <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">Class Standing – 70% <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">Term Examination – 30%
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;"> Quizzes – 30%
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;"> Attendance/Recitation – 20%
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;"> Projects/Assignments – 20%

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">The Final Grade will be computed based on the 50 – 50 policy (50% of the Midterm + 50% of the Tentative Final Grade) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">**References:**
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Barnetee et al. //Calculus for Business Economics, Life Sciences & Social Sciences// (8th Ed.).
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">L. Leithold (1995). //The Calculus// (7th Ed.). Harper Collins Publishers.
 * 3) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Bradley, G. L and Smith, K. J. (1994).  //Calculus with Analytic Geometry,//  4th Ed. Prentice Hall.
 * 4) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Etgen, G., Salas and Hille’s (1995). //Calculs: One and Several Variables,//  7th Ed. John Wiley & Sons, Inc.
 * 5) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Grossman, S. (1992). //Calculus of One Variable,//  3rd Ed. Saunders College Publishing.
 * 6) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Thomas, G. B. & Finney, R. L. (1993). //Calculus and Analytic Geometry,// 8th Ed. Massachusetts: Addison-Wesley.