This first course in calculus emphasizes problem-solving and the application of calculus techniques to a variety of real-world situations.
Instructor: Dr. Abeer Yasin
Course Duration: 4 months
This first course in calculus emphasizes problem-solving and the application of calculus techniques to a variety of real-world situations. The course begins with some preliminary material that reviews the concept of a function and basic problem-solving techniques, and tests a student's preparedness for studying calculus. The five course units include examinations of: secants and tangent lines, velocities and other rates of change, polynomial and trigonometric functions, logarithmic and inverse trigonometric functions, Mean Value Theorem, and derivatives.
After successfully completing this course, the students will be able to:
Find limits of functions graphically, numerically and algebraically.
Analyze and apply the notions of continuity and differentiability to algebraic and transcendental functions.
Determine derivatives by a variety of techniques including explicit differentiation, implicit differentiation, and logarithmic differentiation.
Use these derivatives to study the characteristics of curves.
Construct detailed graphs of nontrivial functions using derivatives and limits.
Use basic techniques of integration to find particular or general anti-derivatives.
Lesson 1: Functions
Lesson 1 focuses on exponential, inverse and logarithmic functions and their applications to real life models.
Lesson 2: Limits and Derivatives
In this lesson we will discuss the tangent and velocity problem, the limit of a function, calculating limits using limit laws, the precise definition of a limit, continuity, limits at infinity and horizontal asymptotes, tangents, velocity, rates of change, derivatives and the derivative as a function.
Lesson 3: Differentiation Rules
Lesson 3 focuses on derivatives of polynomials and exponential functions, the product and quotient rules of differentiation, derivatives of trigonometric functions, the chain rule, implicit differentiation, higher derivatives, derivatives of logarithmic functions and related rates.
Lesson 4: The Mean-Value Theorem
Lesson 4 focuses on the mean value theorem and its applications including increasing and decreasing functions, local extreme values, endpoint and absolute extreme values, max and min problems, concavity and points of inflection, vertical and horizontal asymptotes, curve sketching, velocity and acceleration and related rates of change per unit time problems.
Lesson 5: Applications of Differentiation
In this lesson we discuss a variety of topics as applications of differentiation including maximum and minimum values, the affect of the derivative on the shape of a graph, indeterminate forms and LHospital rule, optimization problems, Newtons method and anti-derivatives.
Textbook: James Stewart, Calculus: Early Transcendentals, fourth edition, Brooks/Cole, 1999.
level of difficulty:
minimum class size:
Avaliable Online by Appointment
|| Calculus I
|| live session
||This first course in calculus emphasizes problem-solving and the application of calculus techniques to a variety of real-world situations.
total duration: 1h 0m over 1 session(s)
|discussion forums: 1|
| Abeer Yasin
description of :
Courses taught on- ground and online:
Fundamentals of Mathematics
Elementary Probability and Statistics
Advanced Business Statistics
Business Mathematics and Economics
Business Statistics and Research
Statistics and Probability
Research and Statistics
Probability and Statistics for Engineers
Mathematics for Medical Students
SPSS and Statistics
Linear Algebra I
Ordinary Differential Equations
Partial Differential Equations
Fundamentals of Accounting I
Fundamentals of Accounting II
Principles of Macroeconomics
Principles of Microeconomics
Quantitative Reasoning for Business (Graduate, Research)
Doctoral Dissertation Courses
DOC 733 A
DOC 734 A
DOC 734 B
Microsoft power point
Latex MiKTeX (2.7)
SPSS Statistical Software.
Graph Pad Prism Statistical Software.
MedCalc Statistical Software
Analyze it for Microsoft Excel Statistical Software
Math Magic Personal 3.64
Equation Conversion Manager
Project Kick Start
LMS Chart Maker
Assistat (Statistical Assistance, v 7.6 beta)
AM Statistical Software (product of the American Institutes of Research, v 0.06)
StatEasy (v 0.4
PQRS (Probabilities, Quantiles and Random Samples)
WinIDAMS (Validation, Manipulation and Statistical Analysis of Data, v 1.3, UNESCO)
InStat (Statistical Services Center, v 3.036)
Mathematics and Engineering:
Nonlinear Partial Differential Equations.
P-Laplace Operator and Applications in Engineering and Medicine
Pure and Applied Mathematics in Medicine:
Statistics and Applied Mathematics in Medicine:
Glomerular Filtration Rate estimation (e-GFR).
Cystatin C and Nephrology.
Cystatin C and Cardiology
GDF-15 (Growth Differentiation Factor-15)
Beta Trace Protein
Modeling of Mathematical Phenomena in Nephrology and Cardiology
's preferred teaching style:
Online-Virtual class room