• Adam Kanigowski Awarded European Mathematical Society Prize

    He is the first member of UMD’s Department of Mathematics to receive this prestigious award for young mathematicians. The European Mathematical Society (EMS) awarded a 2024 EMS Prize to Adam Kanigowski, a Polish-born associate professor in the University of Maryland’s Department of Mathematics. Established in 1992, the prize is presented every four years to… Read More

  • Jonathan Poterjoy and Kayo Ide join new $6.6 million NOAA consortium

    Congratulations to AOSC's Jonathan Poterjoy and Kayo Ide (also of math and IPST) on joining a new NOAA consortium to improve the accuracy of weather forecasts.  Called CADRE, the $6.6 million initiative will focus on data assimilation, which uses observations to improve model predictions of natural systems, like Earth's atmosphere, over time.… Read More

  • Alfio Quarteroni receives the Blaise Pascal Medal in Mathematics

    Congratulations to Alfio Quarteroni for winning the 2024 Blaise Pascal Medal in Mathematics The message from the European Academy of Sciences reads: We are excited to announce that Professor Alfio Quarteroni has been awarded the esteemed 2024 Blaise Pascal Medal in Mathematics for his outstanding contributions to the field, particularly in… Read More

  • Archana Receives the Donna B. Hamilton Award

    Archana Khurana has been selected to receive the Donna B. Hamilton Award for Excellence in Undergraduate Teaching in a General Education Course.  Awards are based solely on student nominations and are solicited from across campus.  From the many nominations received, the selection committee was very impressed by the student experience… Read More

  • Yanir Receives a Do Good Campus Fund Grant

    Yanir’s proposal on “Incorporating outreach into the curriculum via experiential learning” is one of the only 27 projects out of 140 submissions that were funded by the UMD Do Good Campus Fund. Read More
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Description

Introduction to calculus, including functions, limits, continuity, derivatives and applications of the derivative, sketching of graphs of functions, introduction to definite and indefinite integrals, and calculation of area. The course is especially recommended for science and mathematics majors. Credit will be granted for only one of the following: MATH 140 or MATH 136 or MATH 120.

Prerequisites

Permission of the department based on 3 1/2 years of college preparatory mathematics (including trigonometry) and either a satisfactory score on the mathematics placement examination or completion of Math 115 with a grade of C or better.

Topics

Chapter 1. Functions

Brief review of major topics in precalculus

Chapter 2. Limits and Continuity

Limits, one sided and infinite limits
Tangent lines and velocity
Continuity, the Intermediate Value Theorem, and the Bisection Method

Chapter 3. Derivatives

Derivatives, including the Chain Rule
Implicit differentiation
Related rates
Approximation of derivatives and the Newton-Raphson method

Chapter 4. Applications of the Derivative

Maximum and minimum values, and the Maximum-Minimum Theorem
Mean Value Theorem and its applications
Exponential growth and decay
Analysis of graphs of functions

Chapter 5. The Integral

Definite and indefinite integrals
The Fundamental Theorem of Calculus
Integration by substitution
Natural logarithmic function
Area

Chapter 10. Curves in the plane

Basic properties of parabolas, ellipses and hyperbolas

 

Calculator Programs

The course includes an introduction to a few numerical methods, such as Newton's Method for solving nonlinear equations and Riemann sums for approximating integrals. For such methods, it is convenient to use a computer or calculator. Programs for Riemann sums on a TI-83 or TI-84 calculator may be found here. Programs for Newton's method may be found here.

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