This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for elliptic; hyperbolic and parabolic differential operators; method of characteristics; review of Lebesgue integration; distributions; fourier transform; homogeneous distributions; asymptotic methods.

In this course, we study elliptic Partial Differential Equations (PDEs) with variable coefficients building up to the minimal surface equation. Then we study Fourier and harmonic analysis, emphasizing applications of Fourier analysis. We will see some applications in combinatorics / number theory, like the Gauss circle problem, but mostly focus on applications in PDE, like the Calderon-Zygmund inequality for the Laplacian, and the Strichartz inequality for the Schrodinger equation. In the last part of the course, we study solutions to the linear and the non-linear Schrodinger equation. All through the course, we work on the craft of proving estimates.

This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.

'Tricks' tap into children's natural curiosity and can provide the motivation for exploring the underlying mathematics in order to unpick how they are done. This Nrich problem explores a "trick" to provide an engaging context in which to explore place value and in particular 'adding nine' as 'adding ten and subtracting one'.

In this YouCubed task. students examine what happens when you keep continuing a pattern, forever. Students delve into the infinite and find the patterns and their area.

This short video and interactive assessment activity is designed to teach third graders about finding the remainder given the total number and number of groups.

This short video and interactive assessment activity is designed to teach fifth graders about dividing 2-digit numbers by 2-digit numbers.

This short video and interactive assessment activity is designed to teach third graders about dividing by 12.

This Nrich problem uses the idea of sequences in a very tangible form. Children will need to recognize odd and even numbers as well as be able to count fluently both backwards and forwards. They will also have opportunities to justify their answers.

The Nrich game as introduced is intended for children who are just beginning to become confident with small numbers. However there are many variations, some suggested below, that make it suitable for older children. As with many of the NRICH games, consolidation of basic number facts is combined with an element of strategic thinking.

This short video and interactive assessment activity is designed to give fourth graders an overview of speed based problems.

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra. In writing this book I have been guided by the these principles: • An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. • An elementary text can’t be better than its exercises. This text includes 2041 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. • An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and defonitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 299 completely worked out examples. Where appropriate, concepts and results are depicted in 188 figures

CK-12's Grade 5 Elementary Math is a series of videos and interactive videos designed to teach basic math concepts to 5th graders. Concepts covered include Multiplication and Division, Place Value, Multiple Operations and Grouping, Decimals, Time, Fractions, Money, Measurement, and Geometry.

This subject provides an introduction to fluid mechanics. Students are introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of fluids and learn how to solve a variety of problems of interest to civil and environmental engineers. While there is a chance to put skills from Calculus and Differential Equations to use in this subject, the emphasis is on physical understanding of why a fluid behaves the way it does. The aim is to make the students think as a fluid. In addition to relating a working knowledge of fluid mechanics, the subject prepares students for higher-level subjects in fluid dynamics.

This lesson unit is intended to help teachers assess how well students are able to: translate between the equations of circles and their geometric features; and sketch a circle from its equation.

The math learning center is an app and online platform that allows students to use manipulatives virtually. In this activity, students will show equivalent fractions using lines and shapes.

This lesson unit is intended to help you assess how well students are able to: solve simple problems involving ratio and direct proportion; choose an appropriate sampling method; and collect discrete data and record them using a frequency table.

The Number Pieces Basic app helps students develop a deeper understanding of place value while building their competition skills with multi-digit numbers. Students can use the number pieces to represent multi-digit numbers, count, regroup, add, and subtract. The drawing tools allow students to label representations and show their understanding numbers and math concepts.

This article is for elementary teachers putting together fraction units. There is a discussion of activities and misconceptions.

This short video and interactive assessment activity is designed to teach third graders about completing the number patterns based on the multiplication table.