Calculus II is a standard second course in calculus where the focus of the course is integration and its various techniques
Instructor: Dr. Abeer Yasin
Course Duration: 6 months
Calculus II is a standard second course in calculus where topics covered include integration of elementary functions, techniques of integration, integrals with infinite limits of integration, integrals with discontinuous integrands, applications of the definite integral, introduction to sequences and series and their applications.
After successfully completing this course, the students will be able to:
Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems.
Use basic techniques of integration to find particular or general anti-derivatives.
Demonstrate the connection between area and the definite integral.
Apply the Fundamental theorem of calculus to evaluate definite integrals.
Use differentiation and integration to solve real world problems such as rate of change, optimization, and area problems.
Communicate mathematics and explain solutions to problems both verbally and in written sentences.
Lesson 1: An overview of the area problem
Lesson 1 discusses the definite and indefinite integrals. The area under the curve will be expressed as a limit of a Riemann sum. Other topics will include the Fundamental theorem of Calculus and the area between two curves.
Lesson 2: general Integration rules and Integration by substitution
Lesson 2 will discuss the anti-derivative and the general rules of integration as well as integration by substitution as an integration tool and the cases when it can be applied.
Lesson 3: Integration by parts
Lesson 3 will focus on the integration by parts technique as one of the integration tools for indefinite and definite integrals, for integrals involving sine and cosine, integrals involving ln, arcsin, arctan, and integrals involving exponentials.
Lesson 5: Trigonometric Integrals
In lesson 5 we will discuss trigonometric integrals of products of powers of sine and cosine, products of powers of tan and sec and products of sine and cosine and multiples of the variables.
Lesson 6: Trigonometric Substitutions:
Lesson 6 will discuss trigonometric substitutions through completing the square, substitutions involving sine and cosine, substitutions involving tan and substitutions involving sec.
Lesson 7: Integration using partial fractions
This lesson will discuss integration of rational functions through long division of polynomials, decomposition of simple fractions, simple linear factors, repeated linear factors, simple quadratic factors and rationalizing substitution.
Lesson 12: Improper integrals
Lesson 12 will look into the case of integration of an infinite function in an infinite domain of integration, the special case referred to as improper integration.
Textbook Calculus, Early Transcendental Functions, 3rd ed., R. Smith and R. Minton, McGraw-Hill, 2007
level of difficulty:
minimum class size:
Avaliable online by appointment
|| Caclulus II
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||Calculus II is a standard second course in calculus where the focus of the course is integration and its various techniques
total duration: 1h 0m over 1 session(s)
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| 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