THE FUTURE OF PEOPLE BECOMING THE CHURCH: MULTIPLYING DISCIPLES, LEADERS, AND CAMPUSES IN A POST-CHRISTIAN, DE-CHURCHED, AND UNCHURCHED REGION OF THE UNITED STATES

The church is losing influence in America. Furthermore, the COVID-19 pandemic exacerbated the decline in the American church. Polarized on issues of race, politics, masks, and vaccines, church leaders struggled to unite the people of God. Post-pandemic, how do churches and church leaders make more disciples, develop more leaders, and plant more churches in a post-Christian, de-churched, and unchurched culture? The focus of this doctoral dissertation is to present the philosophy of people becoming the church as a solution to the decline of the American church. I discovered the philosophy of people becoming the church over twenty years ago when I planted newlife – a church in the Greater Seattle area. This dissertation is an in-depth study of people becoming the church at newlife and the findings from qualitative research to make people becoming the church more effective in the future. The project concludes with people-becoming-the-church principles that can be adapted and applied to other churches in other contexts. The five people-becoming-the-church principles are as follows: blur the line between people and pastors, creativity sparks evangelism, dive into the community to solve problems, the church can gather anywhere and at any time, and church buildings are assets to the community and are used all week

Finite Difference Schemes for Integral Equations with Minimal Regularity Requirements

Volterra integral equations arise in a variety of applications in modern physics and engineering, namely in interactions that contain a memory term. Classical formulations of these problems are largely inflexible when considering non-homogeneous media, which can be problematic when considering long term interactions of real-world applications. The use of fractional derivative and integral terms naturally relax these restrictions in a natural way to consider these problems in a more general setting. One major drawback to the use of fractional derivatives and integrals in modeling is the regularity requirement for functions, where we can no longer assume that functions are as smooth or as well behaved as their classical counterparts. This work outlines the derivation and application of a class of stable and convergent finite difference methods to discretize weakly singular integrals which occur in Volterra integral equations. This derivation is motivated by classical discretizations that arise in Caputo fractional derivatives. We present a time-fractional diffusion equation as a case study to develop the finite difference scheme, where the Laplace transform is used to pose the problem equivalently as a Volterra integral equation, which is then discretized. A generalized scheme is presented to consider a much wider class of integral equations, which allows for the consideration of applications of the Fourier transform. This ultimately allows for a natural discretization of both time- and space-fractional diffusion and differential equations. Some natural physical applications are considered to fully utilize these schemes. The novelty of these schemes is in its simplicity and efficiency when compared to classic methods of discretization, especially for Caputo fractional derivatives. Typical discretizations in the fractional derivative form over-assume regularity to discretize a full derivative term, which subsequently restricts the admissible solution space. Other considerations from discretizing the fractional derivative form include negatively impacting the rate of convergence from the remaining fractional integration term, which is recovered by the use of non-uniform mesh partitions to recover some of the order of convergence

Typhoid Fever Treated by the Woodbridge Method.

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