MATH 119 Calculus with Analytic Geometry
Frequency: Fall/Spring Terms
Credit: (4-2)5
Catalog description: Functions, Limits, continuity and derivatives.
Applications. Extreme values, the Mean Value Theorem and its applications.
Graphing. The definite integral. Area and volume as integrals. The
indefinite integral. Transcendental functions and their derivatives.
L'Hospital's Rule. Techniques of integration. Improper integrals.
Applications.
Justification for the Course Proposal: This is a fundamental course
designed for all science – Engineering Students.
Course Objectives: The sequence Math 119-120 is the Standard complete
introduction to the concepts and methods of calculus. It is taken by all
engineering students. The emphasis is on concepts, solving problems,
theory and proofs. All sections are given a uniform midterm and a final
exam. Students will develop their reading, writing and questioning skills
in Mathematics.
Course Coordinator: Dr. Muhiddin Uğuz
MidTerm1:
30 Points (Nov 07 2009 Saturday at 09:30)
MidTerm2:
30 Points (Dec 12 2009 Saturday at 09:30)
Final Exam:
40 Points (Jan 14 2010 Thursday at 09:30)
Quiz/Attendance: 10 Points
Suggested textbooks: Calculus James Stewart, Fifth Edition
Reference Books: Robert A. Adams, A Complete Course Calculus. Fifth Edition.
Current Semester Course Home Page: http://www.ma119.metu.edu.tr
Week
1
2
3
4
Dates
Sep 28-Oct 02
Oct 05-09
Oct 12-16
Oct 19-23
Syllabus(Math 119)
1 Functions and Models 10
1.1 Four Ways to Represent a Function 11
1.2 Mathematical Models: A Catalog of Essential Functions 25
1.3 New Functions from Old Functions 38
2 Limits and Rates of Change 64
2.1 The Tangent and Velocity Problems 65
2.2 The Limit of a Function 70
2.3 Calculating Limits Using the Limit Laws 82
2.4 The Precise Definition of a Limit 92
2.5 Continuity 102
2.6 Tangents, Velocities, and Other Rates of Change 112
3 Derivatives 127
3.2 The Derivative as a Function 134
3.3 Differentiation Formulas 145
3.5 Derivatives of Trigonometric Functions 169
3.6 The Chain Rule 175
3.7 Implicit Differentiation 184
3.8 Higher Derivatives 190
3.9 Related Rates 198
3.10 Linear Approximations and Differentials 205
4 Applications of Differentiation 222
4.1 Maximum and Minimum Values 223
5
6
Oct 26-28-30
National Holiday
(National Day /
Cumhuriyet
Bayramı) (October
28, Wednesday
afternoon: Holiday)
Nov 02-06
4.2 The Mean Value Theorem 234
4.3 How Derivatives Affect the Shape of a Graph 240
4.4 Limits at Infinity; Horizontal Asymptotes 249
4.5 Summary of Curve Sketching 263
4.7 Optimization Problems 278
4.10 Antiderivatives 300
Midterm 1(Nov 07, 2009 Saturday at 09:30)
7
8
9
10
11
12
13
14
15
Nov 09-10-13
Anniversary of
Atatürk's Death
(Tuesday)
Nov 16-20
Nov 23-27
Religious HolidayKurban Bayramı
(Arife November 26,
Thursday, Bayram
for 4 days)
Nov 30-Dec 04
Dec 07-11
5 Integrals 314
5.1 Areas and Distances 315
5.2 The Definite Integral 326
5.3 The Fundamental Theorem of Calculus 340
5.4 Indefinite Integrals and the Net Change Theorem 350
5.5 The Substitution Rule 360
6 Applications of Integration 374
6.1 Areas between Curves 375
6.2 Volume 382
6.3 Volumes by Cylindrical Shells 393
6.5 Average Value of a Function 402
7 Inverse Functions: Exponential, Logarithmic, and Inverse
Trigonometric Functions 412
7.1 Inverse Functions 413
7.2 Exponential Functions and Their Derivatives 421
7.2* The Natural Logarithmic Function 451
7.3 Logarithmic Functions 434
7.3* The Natural Exponential Function 460
7.4 Derivatives of Logarithmic Functions 441
7.4* General Logarithmic and Exponential Functions 467
10.4 Exponential Growth and Decay 647
7.5 Inverse Trigonometric Functions 477
Midterm 2(Dec 12, 2009 Saturday at 09:30)
Dec 14-18
Dec 21-25
Dec 28-Jan 01
New Year Holiday
(Friday)
Jan 04-08
7.6 Hyperbolic Functions 486
7.7 Indeterminate Forms and L’Hospital’s Rule 493
8 Techniques of Integration 510
8.1 Integration by Parts 511
8.2 Trigonometric Integrals 518
8.3 Trigonometric Substitution 525
8.4 Integration of Rational Functions by Partial Fractions 532
8.8 Improper Integrals 566
9 Further Applications of Integration 582
9.1 Arc Length 583
9.2 Area of a Surface of Revolution 590
11.3 Polar Coordinates
11.4 Areas and Lengths in Polar Coordinates
Final Exam (Jan 14, 2010 Thursday at 09:30)